Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

Immunity and Arginine Deprivation in Alzheimer's Disease

The pathogenesis of Alzheimer’s disease (AD) is a critical unsolved question, and while recent studies have demonstrated a strong association between altered brain immune responses and disease progression, the mechanistic cause of neuronal dysfunction and death is unknown. We have previously described the unique CVN-AD mouse model of AD, in which immune-mediated nitric oxide is lowered to mimic human levels, resulting in a mouse model that demonstrates the cardinal features of AD, including amyloid deposition, hyperphosphorylated and aggregated tau, behavioral changes and age-dependent hippocampal neuronal loss. Using this mouse model, we studied longitudinal changes in brain immunity in relation to neuronal loss and, contrary to the predominant view that AD pathology is driven by pro-inflammatory factors, we find that the pathology in CVN-AD mice is driven by local immune suppression. Areas of hippocampal neuronal death are associated with the presence of immunosuppressive CD11c+ microglia and extracellular arginase, resulting in arginine catabolism and reduced levels of total brain arginine. Pharmacologic disruption of the arginine utilization pathway by an inhibitor of arginase and ornithine decarboxylase protected the mice from AD-like pathology and significantly decreased CD11c expression. Our findings strongly implicate local immune-mediated amino acid catabolism as a novel and potentially critical mechanism mediating the age-dependent and regional loss of neurons in humans with AD.

There is a large interest in identifying, lineage tracing, and determining the physiologic roles of monophagocytes in Alzheimer’s disease. While Cx3cr1 knock-in fluorescent reporting and Cre expressing mice have been critical for studying neuroimmunology, mice that are homozygous null or hemizygous for CX3CR1 have perturbed neural development and immune responses. There is, therefore, a need for similar tools in which mice are CX3CR1+/+. Here, we describe a mouse where Cre is driven by the Cx3cr1 promoter on a bacterial artificial chromosome (BAC) transgene (Cx3cr1-CreBT) and the Cx3cr1 locus is unperturbed. Similarly to Cx3cr1-Cre knock-in mice, these mice express Cre in Ly6C-, but not Ly6C+, monocytes and tissue macrophages, including microglia. These mice represent a novel tool that maintains the Cx3cr1 locus while allowing for selective gene targeting in monocytes and tissue macrophages.

The study of immunity in Alzheimer’s requires the ability to identify and quantify specific immune cell subsets by flow cytometry. While it is possible to identify lymphocyte subsets based on cell lineage-specific markers, the lack of such markers in brain myeloid cell subsets has prevented the study of monocytes, macrophages and dendritic cells. By improving on tissue homogenization, we present a comprehensive protocol for flow cytometric analysis, that allows for the identification of several cell types that have not been previously identified by flow cytometry. These cell types include F4/80hi macrophages, which may be meningeal macrophages, IA/IE+ macrophages, which may represent perivascular macrophages, and dendritic cells. The identification of these cell types now allows for their study by flow cytometry in homeostasis and disease.

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.