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This dissertation contains the analysis of the general lattice non-stationary Anderson parabolic model with correlated white noise. It starts form the brief description of known results about parabolic problem with local Laplacian and the detailed description of the general non-local Anderson model in the non-stationary random environment (Chapter 2). Chapter 3 is devoted to existence-uniqueness theorems for the parabolic model in the weighted Hilbert space and the solution in Feynman–Kac formula representation. The chapter 4 contains the results on the first and second moments of the solution and the spectral properties of the Hamiltonian $\mathcal{H}_2$, providing the basic information on the phase transition of the model from the regular to intermittent structure, additional results concerns the other spectral bifurcations of $\mathcal{H}_2$.
Progress in nanofabrication made possible development of metamaterials and nanoplamonics two decades ago. The area of mesoscale photonics where the characteristic dimensions of spherical, pyramidal or other building blocks are on the order of several wavelengths remained relatively less studied. However, the optical properties of such structures are extremely interesting due to their ability to create tightly focused beams, so-called “photonic nanojets”, and to resonantly trap light inside their building blocks. In this dissertation, we focus on two main applications of such structures. It is proposed to use dielectric microcons for concentrating light on photodetector focal plane arrays (FPAs) and it is proposed to use contact high-index dielectric microspheres (also termed ball lenses) for improving resolution in cellphone-based microscopy.
We proposed and developed three designs of silicon (Si) microconical arrays which can be used as light concentrators for integration with FPAs operating in mid-infrared (MWIR) region. Such structures can be fabricated by anisotropic wet etching of Si. The spectral and angular dependencies of power enhancement factors (PEFs) provided by such high-index (n~3.5) Si microcones are calculated using finite-difference time-domain modeling. In addition, we observed and studied resonant trapping of photons inside such microcones which can lead to their applications in multispectral imaging devices with a large angle-of-view (AoV).
It is shown that similar microconical light concentrators formed by low-index materials (n = 1.6) which can be fabricated by Nanoscirbe or by plastic injection molding. It is demonstrated that PEFs ~100 times can be achieved in such structures with optimized geometry. It was demonstrated a good agreement of our numerical modeling results with the experiments performed previously on structures with a suboptimal geometry.
We proposed a novel label-free cellphone microscopy assisted by high index contact ball lenses. Resolution of the cellphones is limited by the pixilation of the images. Previous microoptics-based imaging solutions provided insufficient magnification and suffered from spherical aberrations and pincushion distortion. In our work, it is shown that use of ball lenses with n~2 specially designed to provide maximal magnification values (up to 50 times) allows to reduce the role of pixilation and reach diffraction limited resolution values of ~600 nm based on rigorous resolution quantification criteria. It is demonstrated that dispersion properties of the ball lens material significantly influence the magnification in such cellphone imaging. It is shown a semi-quantitative agreement of observed magnification with a simplified geometrical optics model. We demonstrated imaging of various biomedical samples by using proposed cellphone microscopy. It is shown that it can be used as a compact and inexpensive replacement of conventional microscopes to diagnose diseases such as melanoma in vivo without invasive biopsy.
To extend FoV, we assembled centimeter-scale arrays of ball lenses using either micromanipulation or air suction through microhole arrays obtained by laser burning or micromachining. It was found this technology allows obtaining ordered arrays for sufficiently large (>300 μm) ball lenses, but assembling smaller microspheres can in principle be also achieved in future work. It was demonstrated that such microspherical arrays can be used as: a) superresolution coverslips with wide FoV (after embedding in plastic), and b) retroreflectors with ultranarrow reflection cone and highly dispersive properties.
Although the multiracial population is currently the fastest growing racial group in the United States, little remains known about their identity and mental wellness. The purpose of this study was to investigate factors that progress multiracial identity development. More specifically, this study examined the relationship of number of multiracial siblings, sibling phenotype similarity, and sibling relationship quality with the multiracial identity development of multiracial adults. A total sample of 563 multiracial participants were recruited from across the United States and completed an online survey involving self-report questions. The outcome variable of multiracial identity development was measured using the Multiracial Identity Integration Scale. Number of multiracial siblings was measured by a single item on the demographic questionnaire, sibling phenotype similarity was measured by an 11-item scale that the researcher created, and sibling relationship quality was measured by the Lifespan Sibling Relationship Scale. A multiple linear regression analysis and one-way analysis of variance were utilized by the researcher to examine the relationship of the predictor variables with multiracial identity development. The results indicated that none of the predictor variables were found to significantly influence multiracial identity development. Implications of this study include the need for a noticeable increase in research on this identity, counselor trainings and teachings on this population, and the awareness of negative stereotypes about this population still embedded in mental health research and practice. This study provides a starting place for future studies to build upon when investigating multiracial siblings and factors that influence multiracial identity development.
Establishing peaceful post-conflict communities requires returning and reintegrating those who left during the violence. With the United Nations and other institutions investing substantial resources to rebuild communities that have experienced violence with limited success, there is a need to further examine the dynamics of conflict and displacement.
I use a series of field experiments in northeastern Nigeria to examine the impact of exposure to conflict on the decision-making of those in transition communities. The first and second studies explore how war-induced psychological trauma impacts displaced persons' ability to be persuaded to return voluntarily, or formerly displaced persons' to return sustainably. In the third study, I investigate the determinants of the reintegration of former members of violent groups into their communities. In the first two studies, I find that war-related psychological trauma reduces displaced persons' ability to be persuaded. In the third study, I find that contrary to long-held beliefs, traditional leadership efforts to reintegrate former violent members of the community by making peace with them may be counterproductive. Finally, I discussed the academic and policy implications of my findings.
Social networks such as Twitter enable people to interact with each other and share health-related concerns in an effective and novel way, as evidenced during the COVID-19 pandemic when in-person communication became inconvenient under social-distancing policies. Public emotions mined from these social network data have increasingly attracted scholars’ attention because of their significant role in predicting public behaviors. However, little attention has been paid to the impacts of health policy and local political ideology on the trends of spatiotemporal emotions related to COVID-19. This study examines 1) the spatial-temporal clustering trends of negative emotions (or spillover effects); 2) whether health policies such as social distancing policy are associated with spatiotemporal emotion patterns towards COVID-19. This article finds that: COVID-19 related negative emotions detected by social media have spillover effects and that counties with stay-at-home policy or counties that are predominantly democratic exhibit a higher observed number of negative emotions toward COVID-19. These results suggest that scholars and policymakers may want to consider the impacts of interventions caused by public policy and political polarization on spatial-temporal patterns of public health concerns detected by social media.
Based on Aristotle’s philosophy that ethics can be taught, this study examines whether the behavior of licensed accounting professionals is influenced by increased ethics Continuing Professional Education (CPE) required by state licensing boards. Since states are the licensing and oversight bodies of Certified Public Accountants (CPAs), it is important to know what actions state boards have taken to help increase the public trust of the accounting profession, and the efficacy of those actions.
States were selected based on whether they required ethics CPE hours and whether this changed during the study period 2008-2019. Fourteen states were selected (46% of U.S. CPAs). Data was obtained from publicly available resources on the individual state boards’ websites. 7,969 sanctions were hand coded, scored and analyzed for 3 variables: the sanctions rate, severity of acts conducted by CPAs and the severity of sanctions assessed on CPAs.
The results of this study identified inconsistencies in the monitoring and oversight activities of state licensing boards and the variability of publicly available information. Findings suggest that the number of sanctions may be more affected by the level of oversight of state boards of accountancy, driven by resources available to them, than the behavior of regulated accounting professionals.
I have the following three essays in the dissertation:
1. "Does Executive Compensation Duration Generate Different Risk Incentives? Evidence on Corporate Hedging?" coauthored with Jun Chen and Dolly King.
2. "Putable Bonds, Risk-Shifting Problems, and Information Asymmetry," coauthored with Xinde Zhang and Dolly King.
3. "Shareholder-Creditor Conflict and Hedging Policy: Evidence from Mergers between Lenders and Shareholders," coauthored with Yongqiang Chu, Dolly King, and Chen Shen.
To understand why some innovation-driven portfolio firms benefit more from venture capital (VC) funding than others, I explore the salient phenomenon of founder CEO exit. Integrating institutional logics and psychological contracts theories, I propose a meso-level theoretical framework that identifies and explains how an institutional logic of new venture professionalization shapes suboptimal founder CEO exit strategy in portfolio firms. Founder CEO exits may enhance institutional legitimacy, while also fostering contentious relational dynamics that undermine trust and cooperation between founders and venture capitalists; spill over to affect observers; and contribute to a negative sociopolitical climate within portfolio firms. I derive and test hypotheses about the paradoxical effects of founder CEO exit on portfolio firm performance over time and likelihood of failure, including how the conditions of exit – namely, the timing and nature of the exit event – influence those outcomes. I use growth modeling and logistic regression to analyze a unique panel data set of 182 high-technology portfolio firms, founded 1990-2010. Despite mixed empirical results, I found overall support for my proposition: Rigid implementation of founder CEO exit strategy in portfolio firms may improve some short-term metrics of performance (i.e., valuation), while imperiling other longer-term outcomes (i.e., profitability and odds of survival).
In this thesis, we introduce a methodology for the simulation and parameter estimation of multivariate tempered stable distributions. Using the fact that tempered stable distributions can be specified indirectly by a Lévy measure, our approach is based on an approximation due to a discretization of the Lévy measure. We derive this discretization in general and give an explicit construction of the discretization in the bivariate case. Also, our approximation results hold for a wide class of multivariate infinitely divisible distributions.
Based on our main approximation, we develop a method for simulations, which we call the discretization and simulation (DS) method. To demonstrate how well the method works, we perform a series of simulations in the bivariate cases and compare it with another approximate simulation method developed by Rosiński's. Further, we use our discretization for parameter estimation by minimizing the distance between the characteristic function of the multivariate tempered stable distribution and the empirical characteristic function. We then apply our methodology to two bivariate financial datasets related to exchange rates. The first is comprised of exchange rates between standard currencies, while the second is based on exchange rates related to cryptocurrencies. We also perform goodness-of-fit tests to show that the multivariate tempered stable model does a good job fitting the model.
Further, we apply our model for the pricing of the bivariate basket option. Toward this end, we provide theoretical results on the existence of equivalent martingale measures. Then combing this with our model for parameter estimation and the DS method for simulation, we develop a Monte Carlo based method for option pricing. We apply it to the pricing of European call options with different strikes and the pricing of the Multi-asset rainbow option.
