Asymptotic analysis of multiscale approximations to reaction networks

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches to approximation of such models that take the multiscale nature of the system into account. Our primary example is a model of a cell's viral infection for which we apply a combination of averaging and law of large number arguments to show that the ``slow'' component of the model can be approximated by a deterministic equation and to characterize the asymptotic distribution of the ``fast'' components. The main goal is to illustrate techniques that can be used to reduce the dimensionality of much more complex models.Comment: Published at http://dx.doi.org/10.1214/105051606000000420 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Inverse Kinetics Method and Its Application to the Annular Core Research Reactor

The inverse kinetics method, is a method to calculate a reactor’s reactivity profile from its power profile. In this thesis, the reactivity profile corresponding to pulse operations of the Annular Core Research Reactor (ACRR) was sought. Of specific interest was the shutdown reactivity of the reactor following the pulse. This required accounting for delayed beryllium photoneutrons that are present in the ACRR in addition to U-235 delayed neutron precursors. The power profiles of the pulses were experimentally measured using a diamond photoconductive detector (PCD). Using the inverse kinetics equation, a computer code was written to numerically calculate the reactivity corresponding to the PCD signal. It was found that the PCD’s signal was only proportional to the reactor power before and during a pulse. Following a pulse, the PCD lost this proportionality because its response became dominated by fission product and activation gamma rays. Attempts were made to subtract the unwanted gamma ray contribution from the PCD signal. This allowed the reactivity to be roughly determined for tens of seconds following the pulse before the signal strength became too low. The reactivity before and during a pulse could accurately be calculated without the need to correct the PCD signal. This thesis also provides a detailed derivation of the point kinetics equations and inverse kinetics equation, and explores the behavior of the inverse kinetics equation in detail

From the Temporal to the Eternal: The Normative Philosophy of Anselm of Canterbury

The purpose of this thesis is to examine the extent to which Anselm of Canterbury can be described to have possessed a consistent normative philosophy which coherently addressed the question of how the individual ought to act. By so doing it will seek to extend the contemporary commentary of Anselm’s ethical philosophy beyond the abstract and meta-ethical and analyse the ways in which Anselm’s letter collection can be used to show pragmatic approaches to ethical questions. In examining this field, this thesis contains what amounts to two interdependent parts. The first will deal almost exclusively with Anselm’s anthropology, theory of will, and ethical philosophy. The second will, broadly speaking, examine the impact of his theology and ethical philosophy upon his societal and political beliefs. This will by no means amount to an exhaustive study of Anselm’s normative thought; rather, it will provide key examples of how such an approach opens up new lines of research and furthers the field of Anselm studies, addressing several past issues of contention

The effect of noise correlations on randomized benchmarking

Among the most popular and well studied quantum characterization, verification and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a gamma distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes -- consistent with existing experimental data -- highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the Filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.Comment: Updated and expanded to include full derivation. Related papers available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Development of new methods in solid-state NMR

Many chemically important nuclei are quadrupolar with half-integer spin (i.e., spin I = 1.5, 2.5, etc.) The presence of quadrupolar broadening for such nuclei can limit the information that may be extracted using NMR. MAS is able to remove first-order quadrupolar broadening but can only reduce the second-order contribution to the linewidth. The MQMAS and STMAS techniques have enabled high-resolution NMR spectra of half-integer quadrupolar nuclei in the solid state to be obtained by two-dimensional correlation under MAS conditions. Both of these experiments have several well-known limitations. One is that the conversion pulses in particular are very inefficient and the other is that the longer acquisition times required for two-dimensional experiments can be a limiting factor. Both of these disadvantages are addressed in this thesis. For the former case, existing composite pulse schemes designed to improve the efficiency of the conversion of multiple-quantum coherences are compared using 27Al and 87Rb MQMAS NMR of a series of crystalline and amorphous materials. In the latter case, a new experiment, named STARTMAS, is introduced that enables isotropic spectra of spin I = 1.5 spectra to be acquired in real time. The theoretical basis of the technique is explained and its applicability demonstrated using 23Na and 87Rb NMR of a wide range of solids. The nuclear Overhauser effect (NOE) is one of the most widely exploited phenomena in NMR and is now widely used for molecular structure determination in solution. NOEs in the solid state are rare and those to quadrupolar nuclei rarer still, this being due to the general absence of motion on the correct timescale and the usual efficiency of quadrupolar T1 relaxation, respectively. In this thesis, 11B{1H} transient NOE results are presented for a range of solid borane adducts. A comparison is made of the 11B NMR enhancements observed under MAS and static conditions and a rationale is proposed for the behaviour in the latter case

Vermont Foodbank Needs Assessment: An Investigation into the Needs of Community Partners in the Northwest Region of Vermont

Graduate students at the University of Vermont collaborated with the Vermont Foodbank between May and October 2019 to conduct a needs assessment of 20 selected community partners (CPs) in Northwestern Vermont. The purpose of the assessment was to identify firmographics, levels of community engagement, and interest in foodbank initiatives among partner organizations. Surveys were sent to 25 organizations, and 20 were received by the cutoff date of October 21, 2019, resulting in an 80% participation rate. The questionnaire consisted of 27 questions both qualitative and quantitative in nature, consisting of open-ended, multiple-answer, and multiple-choice questions. The survey revealed multiple actions the foodbank can take to better meet the needs of CPs and their constituents. Among them, a noticeable desire to implement a distribution center in Chittenden County, an interest in more fresh produce distribution, and the need to increase awareness of the VT Fresh program. Furthermore, there was a clear difference of perspectives between CPs depending on size, measured by enrollment of volunteers reported. It may be necessary for the foodbank to tailor their initiatives to better suit varying organizational capacity