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Previous electrophysiological studies strongly implicate a role for both alpha (8 – 12 Hz) and gamma (30 – 120 Hz) **oscillations** in selective attention. However, establishing causality requires inducing these **oscillations** in the brain and observing the behavioral changes that result. To this end, we stimulated participants’ right posterior parietal cortex at 10 Hz, 40 Hz or sham while they performed two separate cueing tasks—one endogenous and one exogenous. Stimulation at 40 Hz speeded responses to invalidly-cued targets, suggesting a facilitation of voluntary attentional shifting. There was also a marginal effect of 10 Hz stimulation, such that responses to invalidly-cued targets in the exogenous task were slowed. Possible reasons for a lack of lateralized effects are discussed. These results provide new information about the causal roles of different **frequencies** of neural **oscillation** in facilitating visuospatial attention, providing support for **frequency**-specific effects.

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Complex cognitive abilities, such as memory, require synchronized neural activity across large populations of cells. The hippocampus is a region of the brain required for the formation of long term episodic memories, which is our memory for autobiographical information. The hippocampus itself consists of four sub-regions, the dentate gyrus (DG), CA1, CA2, and CA3, which can be viewed as functionally specialized processing hubs that uniquely contribute to memory formation based on their distinct molecular, synaptic, and anatomical properties. Only together; however, does the collective activity of all four sub-regions provide the neurobiological underpinnings necessary for a functional memory system.
One mechanism for the coordination of neural networks is synchronization through **oscillations**. Neuronal **oscillations** reflect waves of synchronous action potentials and their presence in the hippocampus is strongly associated with episodic learning and memory. Although much progress been made towards understanding how different **frequencies** of activity are generated and how they support hippocampal-based memory, relatively little is known about the role of CA2 in organizing **oscillations**. In this dissertation work, I use combinatorial electrophysiological and chemogenetic approaches to genetically target and manipulate CA2 principal cells to investigate their role in coordinating hippocampal oscillatory networks in awake, behaving mice.
In Chapter 2, I use Designer Receptors Exclusively Activated by Designer Drugs (DREADDs) to manipulate the endogenous G protein-coupled receptor (GPCR) signaling pathways in CA2 while animals explore a novel spatial environment. These experiments revealed that activation or inhibition of CA2 pyramidal cells through the endogenous Gq- and Gi-coupled pathways, respectively, is sufficient to bi-directionally modulate synchronized hippocampal activity in the slow gamma and beta **frequency** ranges.
In Chapter 3, I further dissect the role of CA2 in coordinating hippocampal **oscillations** by inhibiting CA2 pyramidal cells while animals investigate novel social stimuli and record from CA2’s primary output region, CA1. These experiments revealed that the oscillatory structure observed in CA1 is organized in a layer- and **frequency**-specific manner that depends causally on CA2 output. These findings provide evidence that CA2 is an integral processing node capable of coordinating the hippocampal oscillatory networks that support long term episodic memory.

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The linearized Euler equations and the forced Korteweg-de Vries equation are investigated analytically and numerically as models for the behavior of the surface of a fluid flowing over topography and past an obstacle. Dispersionless and linearized variations of the fKdV equation are compared with the full fKdV equation in various parameter regimes. Ways in which information gained from various approximations to the forced Korteweg-de Vries (fKdV) equations predict the behavior of the solution of the full equation are explored. A critical Froude number parameter value above, which stationary solutions exist, is determined and the stability of the stationary solutions is investigated.The behavior of the dispersionless fKdV equation, which is equivalent to a forced, inviscidBurgers equation, is investigated extensively using the method of characteristics. Exact, analytical solution to the dispersionless, nonlinear approximation to fKdV are derived as well as the amplitude and propagation speed of the shocks obtained from the same approximation.The behaviors of the fKdV equation and its variants are investigated and compared for forcing constant in time and forcing with **oscillating** amplitude and position. A Wentzel, Kramers, Brillouin approximation is given for dispersionless KdV with low **frequency** amplitude **oscillation** in the forcing function. An averaging approximation is given for dispersionless KdV with high **frequency** amplitude **oscillation** in the forcing function.The Inverse Scattering Transform is investigated as a diagnostic tool for the behavior of the fKdV equation. The numerical results indicate the emergence of negative eigenvalues of the Schr ̈odinger operator correspond with the emergence of solitons in the solution of the fKdV equation. WKB analysis is used as an application of inverse scattering theory to determine a relationship between the amplitude of the shock in the dispersionless approximation to fKdV and the amplitude of the upstream propagating solitary waves generated by the full equation. All of this information together provides a means of predicting which combinations of parameter values will result in the generation of upstream propagating solitons as well as a novel means of predicting the **frequency** of soliton generation. Multiple numerical methods and their implementations for solving these equations are discussed.
Experiments are carried out in a water recirculating flume and a wave tank. Phenomena predicted by the equations are observed in the experiments and results are compared quantitatively.

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The lightcurves of variable DA and DB white dwarf stars are usually multiperiodic and non-sinusoidal, so that their Fourier transforms show peaks at eigenfrequencies of the pulsation modes and at sums and differences of these **frequencies**. These combination **frequencies** provide extra information about the pulsations, both physical and geometrical, that is lost unless they are analyzed. Several theories provide a context for this analysis by predicting combination **frequency** amplitudes. In these theories, the combination **frequencies** arise from nonlinear mixing of **oscillation** modes in the outer layers of the white dwarf, so their analysis cannot yield direct information on the global structure of the star as eigenmodes provide. However, their sensitivity to mode geometry does make them a useful tool for identifying the spherical degree of the modes that mix to produce them. In this dissertation, we analyze data from eight hot, low-amplitude DAV white dwarfs and measure the amplitudes of combination **frequencies** present. By comparing these amplitudes to the predictions of the theory of Goldreich and Wu, we have verified that the theory is crudely consistent with the measurements. We have also investigated to what extent the combination **frequencies** can be used to measure the spherical degree (ℓ) of the modes that produce them. We find that modes with ℓ > 2 are easily identifiable as high ℓ based on their combination **frequencies** alone. Distinguishing between ℓ = 1 and 2 is also possible using harmonics. These results will be useful for conducting seismological analyses of large ensembles of ZZ Ceti stars, such as those being discovered using the Sloan Digital Sky Survey. Because this method relies only on photometry at optical wavelengths, it can be applied to faint stars using 4 m class telescopes. We present new data from the 4.1 m Southern Astrophysical Research Telescope for the ZZ Ceti star L19-2. We use these data to determine the limits for application of this theory on data from a 4 m class telescope. We also analyze data for the hot, low-amplitude DBV EC 20058-5234 and demonstrate that the theory is applicable to both DAV and DBV white dwarf stars.

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Synchronization is a widespread phenomenon in nonlinear, physical systems. It describes the phenomena of two or more weakly interacting, nonlinear **oscillators** adjust their natural **frequencies** until they come into phase and **frequency** lock. This behavior has been observed in biological, chemical and electronic systems, including neurons, fireflies, and computers, but has not been widely studied in climate. This thesis presents a study of several major examples of synchronized climatic systems, starting with ice age timings seemingly caused by the global climate’s gradual synchronization to the Earth’s 413kyr orbital eccentricity band, which may be responsible for the shift of ice age timings and amplitudes at the Mid-Pleistocene transition. The focus of the thesis, however, is centered the second major example of stable synchronization in the climate system: the continuous, 90 degree phase relationship of the polar climate signals for the entirety of the available ice record. The existence of a relationship between polar climates has been widely observed since ice core proxies became available in both Greenland and Antarctica. However, my work focuses on refining this phase relationship, utilizing it’s linear nature to apply deconvolution and establish an energy transfer function. This transfer function shows a distinctly singular **frequency**, suggesting that climate signal is predominately communicated north to south with a period of 1.6kyrs. This narrows down possible mechanisms of polar connection dramatically, and is further investigated via a collection of intermediate proxy datasets and a set of more contemporary, synchronized, sea surface temperature dipoles. While the former fails to show any strong indication of the nature of the polar signal due in part to the overwhelming uncertainties present on the centennial and millennial scales, the latter demonstrates a large set of synchronized climate **oscillations** exist, communicate in a variety of networks, and have a direct connection to larger climate patterns (in this case, precipitation anomalies). Overall, this thesis represents a clear advance in our understanding of global climate dynamics, presents a new method of climate time series analysis, evidence of 16, stable, synchronized sea surface temperature dipoles, and provides a detailed sediment core database with explanations of age model limitations for future investigation.

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Synchronization is a widespread phenomenon in nonlinear, physical systems. It describes the phenomena of two or more weakly interacting, nonlinear **oscillators** adjust their natural **frequencies** until they come into phase and **frequency** lock. This behavior has been observed in biological, chemical and electronic systems, including neurons, fireflies, and computers, but has not been widely studied in climate. This thesis presents a study of several major examples of synchronized climatic systems, starting with ice age timings seemingly caused by the global climate’s gradual synchronization to the Earth’s 413kyr orbital eccentricity band, which may be responsible for the shift of ice age timings and amplitudes at the Mid-Pleistocene transition. The focus of the thesis, however, is centered the second major example of stable synchronization in the climate system: the continuous, 90 degree phase relationship of the polar climate signals for the entirety of the available ice record. The existence of a relationship between polar climates has been widely observed since ice core proxies became available in both Greenland and Antarctica. However, my work focuses on refining this phase relationship, utilizing it’s linear nature to apply deconvolution and establish an energy transfer function. This transfer function shows a distinctly singular **frequency**, suggesting that climate signal is predominately communicated north to south with a period of 1.6kyrs. This narrows down possible mechanisms of polar connection dramatically, and is further investigated via a collection of intermediate proxy datasets and a set of more contemporary, synchronized, sea surface temperature dipoles. While the former fails to show any strong indication of the nature of the polar signal due in part to the overwhelming uncertainties present on the centennial and millennial scales, the latter demonstrates a large set of synchronized climate **oscillations** exist, communicate in a variety of networks, and have a direct connection to larger climate patterns (in this case, precipitation anomalies). Overall, this thesis represents a clear advance in our understanding of global climate dynamics, presents a new method of climate time series analysis, evidence of 16, stable, synchronized sea surface temperature dipoles, and provides a detailed sediment core database with explanations of age model limitations for future investigation.

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Mitotic chromosomes are known to **oscillate** during prometaphase and metaphase. This study demonstrated that kinetochores move faster in poleward (P) motion than in away-from-the-pole (AP) motion. P and AP motions also showed different position versus time curves, suggesting distinct mechanisms behind the phenomenon. Sister kinetochores **oscillate** with different phases relative to each other. The leading kinetochore usually switches first, from P to AP motion, followed by the trailing one switching from AP to P motion. Such asymmetry and phase lag produces **oscillation** in centromere stretch at twice the **frequency** of individual kinetochores. The leading kinetochore switches after sister chromosomes reach maximum centromere stretch, suggesting tension may trigger the kinetochore switching. To further investigate kinetochore dynamics, K-SHREC (Kinetochore-Speckle High Resolution Co-Localization) was developed to map the relative protein positions within kinetochores using two color fluorescent speckle microscopy, where centroids, orientations and geometries of fluorescent proteins were identified by asymmetric 3D Gaussian fitting in 3D image stacks. The accuracy of this method can reach +/-5nm. The relative positions of kinetochore proteins such as CenpA, Spc24, Spc25, Bub1, DC31, KNL1 and KNL3 to another kinetochore protein Hec1 were assessed in fixed Hela cells at metaphase. When centromeric tension is lost by taxol treatment, Ndc80 complex remains the same orientation and fully extended with 45nm-separation between the N-termini of Hec1 and Spc24. Most proteins moved about 30 nm closer to CENP-A, except Bub1. This result suggests that there is a tension-sensitive linkage between the KNL-1/Mis12 complex/Ndc80 complex (KMN) network of proteins in the core microtubule attachment site and the location of the majority of CENP-A within the peripheral centromere. The Ndc80 complex behaves like a stiff object, perhaps a thin rod. The relative positions between the end of kinetochore microtubule and the centroid of the fluorescent speckle of Hec1 were also measured by imaging GFP-tubulin. A 3D line scan method and an error function fitting algorithm were developed to identify the microtubule end position. Microtubule end stays closer to centromere with about 63nm distance from Hec1.

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The ability to detect biological events at single molecule level provides unique insights in the field of biophysics. Back-focal-plane laser interferometry is a promising technique for single-molecule-scale, 3D position measurements at rates far beyond the capability of video. I present an in-situ calibration method for the back-focal-plane, low-power (non-trapping) laser interferometry. The software-based technique does not rely on any a priori model or calibration knowledge; hence the name Agnostic. The technique is sufficiently fast and non-invasive that the calibration can be performed on the fly, without interrupting or compromising the on-going experiment. The technique can be applied to track 3D, long range motion (up to 100 um) of a broad variety of microscopic biological objects. The spatiotemporal resolution achieved is of the order of a few nanometers and tens of microseconds. Three biological applications enabled by the technique are presented: firstly, a prototype of an **oscillating**-bead high-bandwidth **frequency**-response analyzer for biology, based on Agnostic Tracking as implemented in our custom-built 3D Magnetic Force Microscope (3DFM); secondly, a magnetic-force study that revealed a previously-unknown anchoring-dependent nonlinear response of a cellular membrane; last, a rheological study that revealed a novel grouping of motion characteristics of individual vesicles diffusing inside live cytoplasm.

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Collective pulsing to generate fluid flow is an important phenomenon across different biological scales and systems and is essential for many vital functions. Examples of collective behavior in fluids occur at all levels: from swimming bacteria to fish schools. Often in these systems, the collective behavior (whether it be pulsing, swimming, or something else) is not predetermined but emerges from individual responses to changes in the local environment. Their responses, in turn, alter the environment, creating a feedback loop. In my dissertation, I focus on the collective pulsing behavior and fluid dynamics of xeniid corals (Cnidaria: Alcyonaceae: Xeniidae). First, I isolate the fluid dynamic aspects and describe the characteristic flow patterns generated by the pulsing of an individual coral polyp. Based on these findings, I develop a 3D computational model that I use to investigate the importance of scaling, as determined by the Reynolds number, on the fluid dynamics of coral pulsing. Then, I isolate the behavioral aspect and quantify the patterns of collective behavior. Comparing empirical date to several models, including a random walk model, a Markov chain model, and a coupled phase **oscillators** model, I show that the behavioral patterns observed in pulsing corals can be reproduced by a weakly coupled phase **oscillator** model or an uncoupled phase **oscillator** model with varying intrinsic **frequencies**. Although polyps within a colony are physically connected and share a diffuse nerve net, I find no evidence of information transfer controlling the pulsing behavior between polyps. Finally, I make the first step toward merging collective behavior and fluid dynamics into one model. Using the method of Immersed Boundary with Finite Elements (IBFE), I simulate both single polyps and polyp pairs and compare their flow fields. Additionally, I investigate the effect of phase difference and distance between polyps on the flows generated by polyp pairs. I find no interactions between components of the flow field and conclude that the phase differences and distances between polyps used in my simulations do not result in any significant flow benefit to the polyps. This finding is consistent with the behavioral observations of collective pulsing; from the results in this dissertation, it does not seem that the polyps pulse in a coordinated manner. The contributions of my thesis include the description and quantification of a novel mechanism of mixing displayed by xeniid corals, which could serve as inspiration in the design of small-scale fluid mixers, and the development of a 3D model of collective pulsing behavior, which could be used as a framework to investigate different aspects of coral fluid dynamics and inform decision-making regarding the protection and conservation of corals and coral reefs.

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It is only recently that O.M. Phillips showed that in the presence of an impermeable, non-vertical plane inserted into a stratified fluid creates a parallel shear flow up the plane. The present dissertation combines theoretical, numerical, and experimental extensions of Phillips' work on diffusively driven flows such as time dependence, three-dimensional effects, and optimal shapes. We first develop the governing equations for time-dependent three-dimensional diffusively driven flows in cylindrical pipe geometries. Using Phillips' time independent solutions we non-dimensionalize this system and identify the Schmidt number as the single free parameter. We then consider a simple extension of Phillips' solutions to the time dependent case; the Laplace transform is used to recast the governing equations in the **frequency** domain, where the role of the Schmidt number can be understood. Long time asymptotics for the time dependent system are derived and a principal temporal **frequency** $\\frac{1}{\\sqrt{\\mathrm{Sc}}}$ is identified. A numerical integration of the governing equations reveals that in systems with small Schmidt numbers, this **oscillations** at this **frequency** are prominent in the time evolution. \\indent We then consider the time independent problem for non-planar geometries where the governing system becomes a pair of coupled Poisson's equations. Two methods of solution are developed for this system: first, the system is recast as a pair of uncoupled Fredholm equations of the second kind. The solution to these equations may be expressed as a Neumann series, which converges under certain criteria. In the case that the cross section of the domain is a circle, we are able to separate the solution into radial and angular components which allows us to solve the system exactly, as well as express the general term in the series solution. The qualitative features of both solutions are investigated and their comparison this discussion sheds light on the convergence criteria for the series solution. Another aspect of the three-dimensional problem is the role of geometry in the behavior of the system--- one important quantity which depends on the geometry of the pipe is the mass flux. We investigate the geometric optimization of integral functionals depending on the velocity, density. A criterion is derived for a geometry to be critical (a possible optimizer), and a gradient descent technique based on this criterion is developed and applied to the mass flux integral. We also show that for a certain "golden" radius, the circular cylinder is a critical pipe geometry for the mass flux under the constraint of a fixed cross sectional area. There is also an experimental component to this thesis which will aim to verify the theoretical considerations presented in the first four chapters. Building upon previous work by O.M. Phillips and Peacock et al., we present experimental verification of these flows for three dimensional circular cylinder geometries. We attempt to demonstrate the dependence of these flows on the polar angle of the cylinder using high molecular weight blue dextran as a tracer for the flow. Based on current experimental observations, we suggest interesting directions for future research in this area.

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