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ABSTRACT A system of three tunnel‐coupled quantum dots is considered in the presence of an applied electric field. Given the measurements of differences between ground state energy levels as the electric field is varied, we seek to recover the quantum Hamiltonian matrix that describes this system. We formulate this as an inverse Eigenvalue difference problem and develop algebraic and computational methods along with a warm starting strategy to solve it. The results demonstrate the efficacy of these approaches in the presence of measurement noise. 

Abstract Mouse tracking is an important source of data in cognitive science. Most contemporary mouse tracking studies use binary-choice tasks and analyze the curvature or velocity of an individual mouse movement during an experimental trial as participants select from one of the two options. However, there are many types of mouse tracking data available beyond what is produced in a binary-choice task, including naturalistic data from web users. In order to utilize these data, cognitive scientists need tools that are robust to the lack of trial-by-trial structure in most normal computer tasks. We use singular value decomposition (SVD) and detrended fluctuation analysis (DFA) to analyze whole time series of unstructured mouse movement data. We also introduce a new technique for describing two-dimensional mouse traces as complex-valued time series, which allows SVD and DFA to be applied in a straightforward way without losing important spatial information. We find that there is useful information at the level of whole time series, and we use this information to predict performance in an online task. We also discuss how the implications of these results can advance the use of mouse tracking research in cognitive science. 

Abstract We have previously shown that the time ofChlamydiainfection was crucial in determining the chlamydial infectivity and pathogenesis. This study aims to determine whether the time ofChlamydiainfection affects the genital tract microbiome. This study analyzed mice vaginal, uterine, and ovary/oviduct microbiome with and withoutChlamydiainfection. The mice were infected withChlamydiaat either 10:00 am (ZT3) or 10:00 pm (ZT15). The results showed that mice infected at ZT3 had higherChlamydiainfectivity than those infected at ZT15. There was more variation in the compositional complexity of the vaginal microbiome (alpha diversity) of mice infected at ZT3 than those mice infected at ZT15 throughout the infection within each treatment group, with both Shannon and Simpson diversity index values decreased over time. The analysis of samples collected four weeks post-infection showed that there were significant taxonomical differences (beta diversity) between different parts of the genital tract—vagina, uterus, and ovary/oviduct—and this difference was associated with the time of infection.FirmicutesandProteobacteriawere the most abundant phyla within the microbiome in all three genital tract regions for all the samples collected during this experiment. Additionally,Firmicuteswas the dominant phylum in the uterine microbiome of ZT3Chlamydiainfected mice. The results show that the time of infection is associated with the microbial dynamics in the genital tract. And this association is more robust in the upper genital tract than in the vagina. This result implies that more emphasis should be placed on understanding the changes in the microbial dynamics of the upper genital tract over the course of infection. 

Resistance to treatment, which comes from the heterogeneity of cell types within tumors, is a leading cause of poor treatment outcomes in cancer patients. Previous mathematical work modeling cancer over time has neither emphasized the relationship between cell heterogeneity and treatment resistance nor depicted heterogeneity with sufficient nuance. To respond to the need to depict a wide range of resistance levels, we develop a random differential equation model of tumor growth. Random differential equations are differential equations in which the parameters are random variables. In the inverse problem, we aim to recover the sensitivity to treatment as a probability mass function. This allows us to observe what proportions of cells exist at different sensitivity levels. After validating the method with synthetic data, we apply it to monoclonal and mixture cell population data of isogenic Ba/F3 murine cell lines to uncover each tumor’s levels of sensitivity to treatment as a probability mass function.