The main focus of this dissertation is examining the mechanisms of peripheral B cell tolerance (Chapter 2). Generating a diverse repertoire of B cells reactive against foreign pathogens, yet tolerant to self-tissue, is imperative for an effective immune system. Random gene rearrangement at the immunoglobulin loci results in the majority of newly formed B cells being self-reactive. At an initial checkpoint in the bone marrow, a large portion of self-reactive B cells are rendered unresponsive or are eliminated through apoptosis. A second, less well-defined checkpoint in B cell tolerance occurs in the periphery as developing transitional B cells mature in the spleen. Indeed, studies have shown that rheumatoid arthritis (RA) and systemic lupus erythematosus (SLE) patients have a defect at this second crucial checkpoint. Within the follicle, follicular dendritic cells (FDCs) retain immune complexes and opsonized foreign antigens by Fc and complement receptors, respectively, important for B cell selection during the germinal center response. However, the selection of self-reactive B cells by self-antigen on FDCs has not been addressed. To this end, a mouse model (Cd21cremDELloxp mice) that expresses self-antigen membrane-bound Duck Egg Lysozyme (mDEL) on FDCs to study the fate of mDEL-binding B cells was generated. The results from this model show that self-antigen displayed on FDCs mediates effective elimination of self-reactive B cells at the transitional stage. A portion of Chapter 2 will be on the design and generation of the appropriate mouse model to address the question of peripheral B cell tolerance in late-stage transitional and follicular B cells in the spleen. The remaining half of the chapter will present the results of peripheral B cell tolerance studies in Cd21cremDELloxp mice. Chapter 3 presents work on various aspects of the germinal center reaction including the tools used to study GC B cells, the proteins involved in forming a GC reaction, and exploring mechanisms of eliminating self-reactive B cells that may arise in a GC reaction

Youth navigate the transition into young adulthood by deciding which developmental goals they want to pursue and when to pursue them. While societal expectations shape youths’ decisions on goal choices, goal nomination may change over time based on individual characteristics and life situations. In this study, we used a person-centered approach to identify common profiles of self-reported major developmental goals (N = 462) at two time points: (1) the final year of high school, and (2) four years after high school graduation. Multinomial logistic regression was then used to examine whether factors including work status, values, and demographics predicted latent class membership four years after high school. Results indicated that career and education goals were nominated less frequently over time, while relational and financial goals became more frequently nominated over time. However, the goal categories retained rank-order stability with education and career goals as the most frequently nominated goals at each time point. The Latent Class Analysis revealed four distinct classes of individuals who shared commonality in their goal choice, which was predicted by work status, values, and demographic variables. Findings from this study suggest that there are both general trends and interindividual differences in goal nomination during the transition to adulthood.

The Heisenberg dynamics of the energy, momentum, and particle densities for
fermions with short-range pair interactions is shown to converge to the compressible Euler
equations in the hydrodynamic limit. The pressure function is given by the standard formula
from quantum statistical mechanics with the two-body potential under consideration. Our
derivation is based on a quantum version of the entropy method and a suitable quantum
virial theorem. No intermediate description, such as a Boltzmann equation or semi-classical
approximation, is used in our proof. We require some technical conditions on the dynamics,
which can be considered as interesting open problems in their own right.

We derive the Euler equations from quantum dynamics for a class of fermionic
many-body systems. We make two types of assumptions. The first type are physical
assumptions on the solution of the Euler equations for the given initial data. The second
type are a number of reasonable conjectures on the statistical mechanics and dynamics of
the Fermion Hamiltonian.

We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix
is normalized so that the average spacing between consecutive eigenvalues is of order
$1/N$. We study the connection between eigenvalue statistics on microscopic energy scales
$\eta\ll1$ and (de)localization properties of the eigenvectors. Under suitable assumptions
on the distribution of the single matrix elements, we first give an upper bound on the
density of states on short energy scales of order $\eta \sim\log N/N$. We then prove that
the density of states concentrates around the Wigner semicircle law on energy scales
$\eta\gg N^{-2/3}$. We show that most eigenvectors are fully delocalized in the sense that
their $\ell^p$-norms are comparable with $N^{{1}/{p}-{1}/{2}}$ for $p\ge2$, and we obtain
the weaker bound $N^{{2}/{3}({1}/{p}-{1}/{2})}$ for all eigenvectors whose eigenvalues are
separated away from the spectral edges. We also prove that, with a probability very close
to one, no eigenvector can be localized. Finally, we give an optimal bound on the second
moment of the Green function.