Quantization and the Resolvent Algebra

We introduce a novel commutative C*-algebra of functions on a symplectic vector space admitting a complex structure, along with a strict deformation quantization that maps a dense subalgebra to the resolvent algebra introduced by Buchholz and Grundling \cite{BG2008}. The associated quantization map is a field-theoretical Weyl quantization compatible with the work of Binz, Honegger and Rieckers \cite{BHR}. We also define a Berezin-type quantization map on the whole C*-algebra, which continuously and bijectively maps it onto the resolvent algebra. This C*-algebra, generally defined on a real inner product space X, intimately depends on the finite dimensional subspaces of X. We thoroughly analyze the structure and applicability of this algebra in the finite dimensional case by giving a characterization of its elements and by computing its Gelfand spectrum

Position Effect Takes Precedence Over Target Sequence in Determination of Adenine Methylation Patterns in the Nuclear Genome of a Eukaryote, \u3cem\u3eTetrahymena thermophila\u3c/em\u3e

Approximately 0.8% of the adenine residues in the macronuclear DNA of the ciliated protozoan Tetrahymena thermophila are modified to N6-methyladenine. DNA methylation is site specific and the pattern of methylation is constant between clonal cell lines. In vivo, modification of adenine residues appears to occur exclusively in the sequence 5′-NAT-3′, but no consensus sequence for modified sites has been found. In this study, DNA fragments containing a site that is uniformly methylated on the 50 copies of the macronuclear chromosome were cloned into the extrachromosomal rDNA. In the novel location on the rDNA minichromosome, the site was unmethylated. The result was the same whether the sequences were introduced in a methylated or unmethylated state and regardless of the orientation of the sequence with respect to the origin of DNA replication. The data show that sequence is insufficient to account for site-specific methylation in Tetrahymena and argue that other factors determine the pattern of DNA methylation

Examination and Assessment of Commercial Anatomical E-Learning Tools: Software Usability, Dual-Task Paradigms and Learning

Technological innovation is changing the landscape of higher education, and the competing interests and responsibilities of today’s learners have propelled the movement of post-secondary courses into the online environment. In the anatomical sciences, commercialized e-learning tools have become a critical component for teaching the intricacies of the human body when physical classroom space and cadaveric resources are limited. This dissertation comparatively assessed the impact of two commercial anatomical e-learning tools (1) a simple 2-dimensional e-learning tool (A.D.A.M. Interactive Anatomy) and (2) a complex tool that allows for a 3-dimensional perspective (Netter’s 3D Interactive Anatomy). The comparison was then extended to include a traditional visual-kinesthetic method of studying anatomy (i.e. a physical skeleton). Applying cognitive load theory and working memory limitations as guiding principles, a dual-task assessment with cross over design was used to evaluate cognitive load. Students were assessed using baseline knowledge tests, observation task reaction times (a measure of cognitive load), mental rotation test scores (a measure of spatial ability) and anatomy post-tests (a measure of knowledge recall). Results from experiments carried out in this thesis suggest that the value of commercial anatomical e-learning tools cannot be assessed adequately on the basis of an educator’s, or a software developer’s, intuition alone. Despite the delivery benefits offered by e-learning tools and the positive feedback they often receive, this research demonstrates that neither commercial e-learning tool conferred any instructional advantage over textbook images. In fact, later results showed that the visual-kinesthetic experience of physically manipulating a skeleton yielded major positive impacts on knowledge recall that A.D.A.M. Interactive Anatomy, as a visual only tool, failed to deliver. The results of this dissertation also suggest that the design of e-learning tools can differentially influence students based on their spatial ability. Moreover our results suggest that learners with low spatial ability may also struggle to relate anatomical knowledge if they are examined on contralateral images. By objectively assessing commercial anatomical e-learning tools against traditional, visual-kinesthetic modalities, educators can be confident that the learning tool they select will give their students the best chance to acquire an understanding of human anatomy

Quantitative Reasoning: Individual Differences In Heart Rate and Response Latency

Math is something that all students are required to use at some point during their academic careers. Then they must use it again in the real world. Unfortunately, many students struggle with quantitative processing. In the current study, participants answered first grade level math problems in order to assess cognitive effort when solving math problem. Participants were then assigned randomly to one of two conditions; Answer or Equation. In the Answer Condition participants were asked to solve a series of math problems, whereby they were given a math equation and then they were asked to choose an answer. In the Equation Condition, participants were given the answer, and then they well asked to choose the math equation to which the answer corresponds. The participants’ heart rate (HR) was recorded concurrently as well as their corresponding response latency (RL). It was hypothesized that participants in the Equation Condition would have greater evoked HR (acceleration) and faster RL compared to the Answer Condition. This hypothesis was supported. Moreover, it is predicted that the magnitude of evoked HR will be predictive of RL. It is argued the greater the evoked HR, the greater cognitive effort (encoding) the faster the RL. Although not statistically significant, the trends were in the hypothesized direction

ECOLOGICAL AND EVOLUTIONARY DYNAMICS OF PLANT-SOIL FEEDBACKS: INFLUENCES ON EVOLUTION AND RANGE DYNAMICS

Plants interact with, modify, and are affected by their soil environments. Though plant-soil interactions are well known to be important and active regulators of ecosystem function and community structure, much less is known about how these interactions affect plant evolution. The primary goal of my dissertation was to examine plant-soil interactions under a range of ecological and evolutionary contexts to better understand patterns of biodiversity, ecosystem function, and whole system responses to environmental change. Taking such an eco-evolutionary perspective allows for a holistic understanding of the causes and consequences of complex abiotic and biotic interactions that link ecosystem ecology and evolution. In my first chapter, I reviewed what is known about genetic interactions between plants, soils, and soil communities, and in doing so, identified a new mechanism for how genetically based plant-soil feedbacks might emerge at large scales. In my second chapter, I used field observations and multiple experimental approaches to test whether soil N acts as a selective gradient on plant phenotypes, if soil microbial communities mediate the selective pressure, and whether plant genetic variation impacts soil N pools. In my third chapter, I developed climate and soil ecological niche models, combined with a new double quantile regression approach, to tests how traits are adapted or plastic at critical environmental limits. Finally, my fourth chapter examined how plant-soil interactions and feedbacks at landscape scales may influence range dynamics and associated ecosystem processes as species move upwards towards higher elevations with rising temperatures. Overall, my dissertation sought to bring an evolutionary perspective to ecosystem ecology research by investigating the genetic mechanisms and outcomes of plant-soil interactions

Noncompact uniform universal approximation

The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb R^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden layer, for all continuous activation functions $\varphi\neq0$ with asymptotically linear behaviour at $\pm\infty$. When $\varphi$ is moreover bounded, we exactly determine which functions can be uniformly approximated by neural networks, with the following unexpected results. Let $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ denote the vector space of functions that are uniformly approximable by neural networks with $l$ hidden layers and $n$ inputs. For all $n$ and all $l\geq2$, $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ turns out to be an algebra under the pointwise product. If the left limit of $\varphi$ differs from its right limit (for instance, when $\varphi$ is sigmoidal) the algebra $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ ($l\geq2$) is independent of $\varphi$ and $l$, and equals the closed span of products of sigmoids composed with one-dimensional projections. If the left limit of $\varphi$ equals its right limit, $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ ($l\geq1$) equals the (real part of the) commutative resolvent algebra, a C*-algebra which is used in mathematical approaches to quantum theory. In the latter case, the algebra is independent of $l\geq1$, whereas in the former case $\overline{\mathcal{N}_\varphi^2(\mathbb R^n)}$ is strictly bigger than $\overline{\mathcal{N}_\varphi^1(\mathbb R^n)}$.Comment: 9 pages, 2 figure

C*-algebraic results in the search for quantum gauge fields

This thesis consists of two parts, both situated in operator theory, and both motivated by the quest for rigorous quantizations of gauge theories. The first part is based on [Skripka,vN - JST 2022], [van Suijlekom,vN - JNCG 2021], and [van Suijlekom,vN - JHEP 2022], and concerns the spectral action of noncommutative geometry and its perturbative expansions. We prove the existence of a higher-order spectral shift function under the relative Schatten class assumption, give a converging series expansion of the spectral action in terms of Chern--Simons and Yang--Mills forms, and show one-loop renormalizability of the spectral action in a generalized sense. The second part is based on [Stienstra,vN 2020] and [vN - LMP 2022] and concerns a non-perturbative approach to quantum gauge theory by means of Hamiltonian lattice gauge theory and strict quantization. We construct C*-algebras of U(1)^n-gauge observables on the lattice, show that they are conserved under the relevant time evolutions, construct continuum limit C*-algebras, and show that the result constitutes a strict deformation quantization.Comment: PhD thesis. 149 pages, 3 figure