A Prescription for the Future of Religious Studies: Second-Order Tradition and the Spirit of Modern Science

An examination of the efficacy of religious studies scholarship through a Kuhnian lens.

Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.

First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system,

and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons.

Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons.

Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively.

Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses

and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital

stability but no $L_2$ stability.

Integrated pathway and epistasis analysis reveals interactive effect of genetic variants at TERF1 and AFAP1L2 loci on melanoma risk.

Genome-wide association studies (GWASs) have characterized 13 loci associated with melanoma, which only account for a small part of melanoma risk. To identify new genes with too small an effect to be detected individually but which collectively influence melanoma risk and/or show interactive effects, we used a two-step analysis strategy including pathway analysis of genome-wide SNP data, in a first step, and epistasis analysis within significant pathways, in a second step. Pathway analysis, using the gene-set enrichment analysis (GSEA) approach and the gene ontology (GO) database, was applied to the outcomes of MELARISK (3,976 subjects) and MDACC (2,827 subjects) GWASs. Cross-gene SNP-SNP interaction analysis within melanoma-associated GOs was performed using the INTERSNP software. Five GO categories were significantly enriched in genes associated with melanoma (false discovery rate ≤ 5% in both studies): response to light stimulus, regulation of mitotic cell cycle, induction of programmed cell death, cytokine activity and oxidative phosphorylation. Epistasis analysis, within each of the five significant GOs, showed significant evidence for interaction for one SNP pair at TERF1 and AFAP1L2 loci (pmeta-int  = 2.0 × 10(-7) , which met both the pathway and overall multiple-testing corrected thresholds that are equal to 9.8 × 10(-7) and 2.0 × 10(-7) , respectively) and suggestive evidence for another pair involving correlated SNPs at the same loci (pmeta-int  = 3.6 × 10(-6) ). This interaction has important biological relevance given the key role of TERF1 in telomere biology and the reported physical interaction between TERF1 and AFAP1L2 proteins. This finding brings a novel piece of evidence for the emerging role of telomere dysfunction into melanoma development.

Bridging the Scale Gap from Leaf to Canopy in Biosphere-Atmosphere Gas and Particle Exchanges

Terrestrial ecosystems, occupying more than 25% of the Earth's surface, can serve as

`biological valves' in regulating the anthropogenic emissions of atmospheric aerosol

particles and greenhouse gases (GHGs) as responses to their surrounding environments.

While the signicance of quantifying the exchange rates of GHGs and atmospheric

aerosol particles between the terrestrial biosphere and the atmosphere is

hardly questioned in many scientic elds, the progress in improving model predictability,

data interpretation or the combination of the two remains impeded by

the lack of precise framework elucidating their dynamic transport processes over a

wide range of spatiotemporal scales. The diculty in developing prognostic modeling

tools to quantify the source or sink strength of these atmospheric substances

can be further magnied by the fact that the climate system is also sensitive to the

feedback from terrestrial ecosystems forming the so-called `feedback cycle'. Hence,

the emergent need is to reduce uncertainties when assessing this complex and dynamic

feedback cycle that is necessary to support the decisions of mitigation and

adaptation policies associated with human activities (e.g., anthropogenic emission

controls and land use managements) under current and future climate regimes.

With the goal to improve the predictions for the biosphere-atmosphere exchange

of biologically active gases and atmospheric aerosol particles, the main focus of this

dissertation is on revising and up-scaling the biotic and abiotic transport processes

from leaf to canopy scales. The validity of previous modeling studies in determining

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the exchange rate of gases and particles is evaluated with detailed descriptions of their

limitations. Mechanistic-based modeling approaches along with empirical studies

across dierent scales are employed to rene the mathematical descriptions of surface

conductance responsible for gas and particle exchanges as commonly adopted by all

operational models. Specically, how variation in horizontal leaf area density within

the vegetated medium, leaf size and leaf microroughness impact the aerodynamic attributes

and thereby the ultrane particle collection eciency at the leaf/branch scale

is explored using wind tunnel experiments with interpretations by a porous media

model and a scaling analysis. A multi-layered and size-resolved second-order closure

model combined with particle

uxes and concentration measurements within and

above a forest is used to explore the particle transport processes within the canopy

sub-layer and the partitioning of particle deposition onto canopy medium and forest

oor. For gases, a modeling framework accounting for the leaf-level boundary layer

eects on the stomatal pathway for gas exchange is proposed and combined with sap

ux measurements in a wind tunnel to assess how leaf-level transpiration varies with

increasing wind speed. How exogenous environmental conditions and endogenous

soil-root-stem-leaf hydraulic and eco-physiological properties impact the above- and

below-ground water dynamics in the soil-plant system and shape plant responses

to droughts is assessed by a porous media model that accommodates the transient

water

ow within the plant vascular system and is coupled with the aforementioned

leaf-level gas exchange model and soil-root interaction model. It should be noted

that tackling all aspects of potential issues causing uncertainties in forecasting the

feedback cycle between terrestrial ecosystem and the climate is unrealistic in a single

dissertation but further research questions and opportunities based on the foundation

derived from this dissertation are also brie

y discussed.