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Regularity and Monotonicity for Solutions to a Continuum Model of Epitaxial Growth with Nonlocal Elastic Effects
No full textWe study the following parabolic nonlocal 4-th order degenerate equation: ut= – [2πH (ux) + ln(uxx + α) + 3/2(uxx + α)2]xx, arising from the epitaxial growth on crystalline materials. Here H denotes the Hilbert transform, and α \u3e 0 is a given parameter. By relying on the theory of gradient flows, we first prove the global existence of a variational inequality solution with a general initial datum. Furthermore, to obtain a global strong solution, the main difficulty is the singularity of the logarithmic term when uxx + α approaches zero. Thus we show that, if the initial datum u0 is such that (u0)xx + α is uniformly bounded away from zero, then such property is preserved for all positive times. Finally, we will prove several higher regularity results for this global strong solution. These finer properties provide a rigorous justification for the global-in-time monotone solution to the epitaxial growth model with nonlocal elastic effects on vicinal surface
SynapseJ: An Automated, Synapse Identification Macro for ImageJ
Get PDFWhile electron microscopy represents the gold standard for detection of synapses, a number of limitations prevent its broad applicability. A key method for detecting synapses is immunostaining for markers of pre- and post-synaptic proteins, which can infer a synapse based upon the apposition of the two markers. While immunostaining and imaging techniques have improved to allow for identification of synapses in tissue, analysis and identification of these appositions are not facile, and there has been a lack of tools to accurately identify these appositions. Here, we delineate a macro that uses open-source and freely available ImageJ or FIJI for analysis of multichannel, z-stack confocal images. With use of a high magnification with a high NA objective, we outline two methods to identify puncta in either sparsely or densely labeled images. Puncta from each channel are used to eliminate non-apposed puncta and are subsequently linked with their cognate from the other channel. These methods are applied to analysis of a pre-synaptic marker, bassoon, with two different post-synaptic markers, gephyrin and N-methyl-d-aspartate (NMDA) receptor subunit 1 (NR1). Using gephyrin as an inhibitory, post-synaptic scaffolding protein, we identify inhibitory synapses in basolateral amygdala, central amygdala, arcuate and the ventromedial hypothalamus. Systematic variation of the settings identify the parameters most critical for this analysis. Identification of specifically overlapping puncta allows for correlation of morphometry data between each channel. Finally, we extend the analysis to only examine puncta overlapping with a cytoplasmic marker of specific cell types, a distinct advantage beyond electron microscopy. Bassoon puncta are restricted to virally transduced, pedunculopontine tegmental nucleus (PPN) axons expressing yellow fluorescent protein. NR1 puncta are restricted to tyrosine hydroxylase labeled dopaminergic neurons of the substantia nigra pars compacta (SNc). The macro identifies bassoon-NR1 overlap throughout the image, or those only restricted to the PPN-SNc connections. Thus, we have extended the available analysis tools that can be used to study synapses in situ. Our analysis code is freely available and open-source allowing for further innovation
The Nucleus Accumbens and Ventral Pallidum Exhibit Greater Dopaminergic Innervation in Humans Compared to Other Primates
No full textRecent evidence suggests that increased dopaminergic signaling within the dorsal striatum played a central role in the evolution of the human brain. This increase has been linked to human prosociality and language in what has been described as a dopamine-dominated striatum personality style. Increased striatal dopamine is associated with an increase in ventral striatal activity and promotes externally driven behaviors, including cooperation and social conformity. In contrast, decreased striatal dopamine is associated with increased dorsal striatal activity and favors internally driven and goal-oriented behaviors. Previous comparative studies have focused on the dorsal striatum, measuring dopaminergic innervation in the dorsal and medial caudate nucleus and putamen. Here, we add to this knowledge by examining regions of the ventral striatum. We quantified the density of tyrosine hydroxylase–immunoreactive axons, as a measure of dopaminergic innervation, in the nucleus accumbens and ventral pallidum of humans, great apes, platyrrhine and cercopithecid monkeys. Our data show that humans have a significantly greater dopaminergic innervation in both structures, supporting the hypothesis that selection for a prosocial neurochemistry in the human basal ganglia may have contributed to the evolution of our uniquely social behavior profile
Battling Two Pandemics: The Intersection of Covid-19 and Systemic Racism in San Antonio Schools
Get PDFIn this thesis, I investigate educators’ experiences and observations of structural inequities during the switch to online teaching and learning amidst the COVID-19 pandemic. Through interviews with ten educators in the city of San Antonio, Texas, I analyzed the COVID-19 pandemic through an equity lens, specifically highlighting the ways in which it is transforming access to education for underserved students. Through this study, I find that the digital divide is still a salient issue in society, and that students of color and/or from low socioeconomic backgrounds are pushed out of schools by external structural forces that further marginalize their community. This study highlights the need to develop more culturally competent curricula, prepare critically conscious educators, and take a holistic approach to the education of the next generations
Multi-Scale Dynamical Analysis on Circadian Rhythms of \u3cem\u3eArabidopsis thaliana\u3c/em\u3e
Get PDFAdapting to the 24-hour periodic environment on the Earth, plants have evolved sets of chemical reactions that regulate their circadian rhythms. A number of research groups studying these circadian reactions in the common laboratory plant Arabidopsis thaliana have developed eleven, increasingly elaborate, chemical kinetic models based on genetic feedback loops. Each model consists of a system of coupled nonlinear ordinary differential equations. We find these models are all situated near a Hopf bifurcation in parameter space. This suggests that there may be some biological significance corresponding to this mathematical property.
To study the properties of these systems related to the Hopf bifurcation, we first numerically compute the solutions to the kinetic models for Arabidopsis thaliana. At the whole plant scale, we perform a weakly nonlinear analysis, the Reductive Perturbation Method, on each model near bifurcation to predict the amplitude and frequency of the oscillating concentration of chemical species from the Stuart-Landau amplitude equation. By scaling the numerical frequencies and amplitudes by our theoretical predictions, we show that the solutions to all these models collapse into a universal parameter-free form. Then, we implement Gillespie’s Stochastic Simulation Algorithm to simulate the system at the single-cell level and account for random fluctuations in molecule numbers. We relate the two approaches and discuss some implications of our results for improving future modeling efforts to ensure that the models are consistent with each other and with the dynamics of the Arabidopsis thaliana circadian rhythms. Finally, we comment on the possible biological significance of the models\u27 mathematical features
Classical Simulations of Ultracold Chemical Reactions
Get PDFUsing an 8th order symplectic integration routine, we develop a program which calculates the trajectories of N particles in a D-dimensional phase space. These trajectories are analyzed to determine the lifetime of the transient collision complex specifically for a K+K+Rb collision in 1 dimension. These results are compared with quasiclassical Rice-Ramsperger-Kassel-Marcus (RRKM) Theory lifetime approximations to further validate this theory. Additionally the Fast Lyapunov Indicator is calculated for the system to definitively determine under what conditions the reactants and products behave chaotically or regularly
Narrativas de Aprendizaje y Formación en la Literatura Latinoamericana Reciente
No full textThis thesis analyzes coming-of-age narratives in recent Latin-American novels. It also explores issues such as sexual identity, gender roles, political unrest and the immigrant experience as they relate to the studied bildungsroman narratives
A Longitudinal Study of the Actual Value of Big Data and Analytics: The Role of Industry Environment
No full textDespite the popularity of big data and analytics (BDA) in industry, research regarding the economic value of BDA is still at an early stage. Little attention has been paid to quantifying the longitudinal impact of organizational BDA implementation on firm performance. Grounded in organizational learning theory, this study empirically demonstrates the impact of BDA implementation on organizational performance and how industry environment characteristics moderate the BDA-performance relationships. Using secondary data regarding BDA implementation from 2010 to February 2020, we find that BDA implementation has a significant impact on two types of business value creation: operational efficiency and business growth. Furthermore, the impact of BDA on operational efficiency is amplified in less dynamic and complex environments, while the BDA-business growth relationship is more pronounced in more dynamic, complex, and munificent environments. Collectively, this study provides a theory-centric understanding of BDA\u27s economic benefits. The findings offer insights to firms about what actual benefits BDA implementation may generate and how firms may align the use of BDA with the industry environments they are operating in
\u27Let Me See What I Could Do\u27: Students\u27 Epistemic Affect When Solving Open-Ended, Real-World Problems
Get PDFThis full research paper examines students’ epistemic affect, or their feelings about and within the doing of engineering, when encountering ill-defined problems in two of their first engineering science courses. Ill-defined problems are what students will encounter as professional engineers, but engineering students typically get little practice in their coursework at solving these types of problems. As students explained how they worked their way through the ill-defined and open-ended problems, we found evidence of both positive and negative feelings that arose, as well as descriptions of affective transitions, or shifts from one affect to another. Some of these transitions show evidence that students begin to regulate or anticipate these feelings as a result of repeated exposure to ill-defined problems. This work has implications for including the development of epistemic regulation as part of engineering students\u27 preparation for professional practice