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Katelyn Plaisier Leisman

Publications and source records attributed to Katelyn Plaisier Leisman.

4 recordsLinked to original sources

Data Analysis and Modeling for Transitioning Between Laboratory Methods for Detecting SARS-CoV-2 in Wastewater

Wastewater surveillance has proven to be a useful tool to monitor pathogens such as SARS-CoV-2 as it is a nonintrusive way to survey the potential disease burden of the population contributing to a sewershed. With the expansion of this field since the beginning of the COVID-19 pandemic, laboratory methods to process wastewater and quantify pathogen nucleic acid levels have improved as technologies changed, efforts expanded in size and scope, and supply chain issues were resolved. Maintaining data continuity is crucial for labs undergoing method transitions to accurately assess infectious disease levels over time and compare measured RNA concentrations to public health data. Despite the dynamic nature of laboratory methods and the necessity to ensure uninterrupted data, to our knowledge there has not been a study that unites two datasets from different lab methods for pathogen quantification from environmental samples. Here, we describe a lab transition from SARS-CoV-2 RNA quantification using a low-throughput, manual filtration-based wastewater concentration and RNA extraction followed by qPCR to a high-throughput, automated magnetic bead-based concentration and extraction followed by dPCR. During the two-month transition period, wastewater samples from across the Chicago metropolitan area were processed with both methods in parallel. We evaluated a variety of regression models to relate the RNA measurements from both methods and found a log-log model was most appropriate after removing outliers and discrepancy points to improve model performance. We also evaluated the consequences of assigning values to samples that were below the detection limit. Our study demonstrates that data continuity can be maintained throughout a transition of laboratory methods if there is a sufficient period of overlap between the methods for an appropriate model to be constructed to relate the datasets.

q-bio.QM↗

Improved effective linearization of nonlinear Schrödinger waves by increasing nonlinearity

From among the waves whose dynamics are governed by the nonlinear Schrödinger (NLS) equation, we find a robust, spatiotemporally disordered family, in which waves initialized with increasing amplitudes, on average, over long time scales, effectively evolve as ever more weakly coupled collections of plane waves. In particular, the relative amount of energy contained in their coupling decays to zero with increasing wave amplitude.

nlin.PS↗

Stability of Traveling wave solutions of Nonlinear Dispersive equations of NLS type

In this paper we present a rigorous modulational stability theory for periodic traveling wave solutions to equations of nonlinear Schrödinger (NLS) type. We first argue that, for Hamiltonian dispersive equations with a non-singular symplectic form and $d$ conserved quantities (in addition to the Hamiltonian), one expects that generically ${\mathcal L}$, the linearization around a periodic traveling wave, will have a $2d$ dimensional generalized kernel, with a particular Jordan structure: The kernel of ${\mathcal L}$ is expected to be $d$ dimensional, the first generalized kernel is expected to be $d$ dimensional, and there are expected to be no higher generalized kernels. The breakup of this $2d$ dimensional kernel under perturbations arising from a change in boundary conditions dictates the modulational stability or instability of the underlying periodic traveling wave. This general picture is worked out in detail for the case of equations of NLS type. We give explicit genericity conditions that guarantee that the Jordan form is the generic one: these take the form of non-vanishing determinants of certain matrices whose entries can be expressed in terms of a finite number of moments of the traveling wave solution. Assuming that these genericity conditions are met we give a normal form for the small eigenvalues that result from the break-up of the generalized kernel, in the form of the eigenvalues of a quadratic matrix pencil. We compare these results to direct numerical simulation in a number of cases of interest: the cubic and quintic NLS equations, for focusing and defocusing nonlinearities, subject to both longitudinal and transverse perturbations. The longitudinal stability of traveling waves of the cubic NLS has been previously studied using the integrability: in this case our results agree with those in the literature. All of the remaining cases appear to be new.

math.AP↗

Linearizable boundary value problems for the nonlinear Schrodinger equation in laboratory coordinates

Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions to initial-value problems on the infinite line, either explicitly or by constructing a suitable Backlund transformation. Various soliton solutions are explicitly constructed and studied.

nlin.SI↗