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Following the trend in portable wireless communications, this dissertation explores new approaches to designing of power-critical building blocks in the elementary circuit level. Specifically, the work focuses on designs of baseband continuous-time Gm-C filter, LC-resonator quadrature **oscillators**, transistor-only quadrature **oscillators** and LC-resonator **frequency** dividers. The established circuits share a common design objective of low-power and low-voltage operation, where the simplicity of the demonstrated topologies serves as a basis. The dissertation is separated in two parts. The first part is dedicated for the baseband section where a 3rd-order Bessel filter is designed and fabricated. The filter comprises a set of linear transconductors, which each one is based on the operation of triode-biased transistors. According to the operation in this region and to the simplicity of the transconductor, high dynamic range can be achieved for a supply voltage as low as 1.2 V. In the other part, attempts in reducing the power consumption of two critical building blocks in a **frequency** synthesizer, namely, the quadrature **oscillator** and the first-stage **frequency** divider, are introduced. For the **oscillators**, two quadrature **oscillators** based on LC resonators are presented, in conjunction with a transistor-only quadrature **oscillator**. Quadrature signal generations in these designs are achieved by making use of the principles of ring **oscillator** and coupled **oscillator**. The last building block that is designed in this part is the LC-based injection-locked **frequency** divider. The single-ended Colpitts **oscillator** topology is used as the core circuit of the divider due to its simplicity and low-voltage property. Detailed analysis concerning the phase relationship between the input and the output leads to the implementations of differential and quadrature divider configurations. Although a silicon integration is done only for the baseband filter, the concept, the operation and the theories developed for the quadrature **oscillators** and the **frequency** dividers have been verified against simulations and measurements employing low-**frequency** discrete prototypes. As they are illustrated in each chapter, the established theories match closely to the measurements.

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A program of research has been undertaken to examine the interaction between vortex shedding and the galloping type **oscillation** which square cylinders are subject to when immersed in a water stream. It is possible that the fluctuating force from the vortex shedding could quench the galloping **oscillation** if it acts as a forced **oscillation** (independent of cylinder motion). An experiment was designed where a square cylinder with one degree of freedom could **oscillate** transversely to the water flow. The amplitude and **frequency** of the cylinder **oscillation** were measured. By using a hot film anemometer spectra of the fluctuating velocity in the wake were taken to determine what **frequencies** vortex shedding occurred at. The results show that for velocities greater than the resonant velocity the galloping **oscillation** is dominant and the cylinder motion controls the **frequencies** of the wake. For velocities less than the resonant velocity no galloping occurs and the vortex shedding seems to control any cylinder motion which occurs. To explain this type of response a mathematical model has been constructed. The model is a set of two coupled self excited **oscillators**} one with the characteristics of the galloping **oscillation** and the other with the characteristics of the fluctuating lift force from the vortex shedding. Using the model some aspects of the observed interaction are explained.

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Brain-Behavior Relations
Scatterplots with regression lines showing significant correlation of drug impact on poststimulus alpha/beta spatial attention effects with inverse efficiency scores for parieto-occipital cortex (see Figures 2E, 2F, and S1).
(A) Correlation with the lateral parts of parieto-occipital cortex (Figure 2F, 10–20 Hz, 0–200 ms).
(B) Correlation with an ROI in the parieto-occipital sulcus (Figure S1), a structure tightly linked with alpha **oscillations** at the t-f window where the drug effect is maximal there (5–15 Hz, 0–350 ms).
Difference of attentional lateralization (Attention Left minus Attention Right) in power for right minus left hemispheres are shown on the y axis, differences of inverse efficiency is shown on the x axis. Each point gives difference scores for one participant, in blue the subjects where the drug session followed placebo and in green where drug preceded placebo. Negative values on the x and y axis indicate stronger effects in the expected direction (stronger hemispheric lateralization and faster processing for the physostigmine condition). Subjects for whom the drug was administered in the second session tend to have stronger effects. See also Figure S3.
... Spatial Attention and Alpha/Beta **Oscillations**
(A) Time-**frequency** (t-f) profile for effect of spatial attention in the placebo session for symmetric hemispheric lateralization effects of Attention Left minus Attention Right at low **frequency** **oscillations**. Time zero corresponds to target onset in this and all subsequent t-f plots, and the color bar indicates t values. The t-f plot combines analogous effects in the left and right hemisphere.
(B) The topography reveals suppressed/enhanced alpha/beta power (t-f window marked in A) in the hemisphere contralateral/ipsilateral to the attended hemifield, as expected (blue colors represent suppression, red enhancement).
(C and D) T-f profile for corresponding effect of spatial attention in the physostigmine condition, with topography shown in (D); note the enhanced effect compared with (A) and (B).
(E) T-f profile for the direct contrast of spatial attention effect in physostigmine minus placebo conditions, with topography shown in (F).
(F) The cholinergic enhancement is localized to parieto-occipital cortex, an area tightly linked to alpha **oscillations** (see also Figure S1 for closer investigation of the parieto-occipital sulcus). Topographies are thresholded at p < 0.05, uncorrected, but for symmetric voxel pairs (see Experimental Procedures).
... Spatial Attention and Gamma **Oscillations**
(A) Time-**frequency** profile for symmetric hemispheric lateralization effects of Attention Left minus Attention Right for high **frequency** **oscillations** under placebo.
(B and C) Topography of the high-**frequency** spatial attention effects under placebo for the time-**frequency** window marked in (A), shown in posterior view (B) or shown in ventral view (C), i.e., seen from below. Note that hot colors in the topographies indicate enhanced power contralateral to the attended hemifield, cold colors indicate reduced power ipsilateral to the attended hemifield.
(D–F) Corresponding data now shown under physostigmine. Note the high reproducibility of the spatial attention effects on gamma, identical under drug/placebo. As a consequence there was no significant enhancement of gamma attention effects by the drug (the nonsignificant trend was actually for slightly stronger gamma attention effects under placebo). All values plotted are t values for the contrast of Attention Left minus Attention Right.
Topographies are thresholded at p < 0.05, uncorrected, but for symmetric voxel pairs (see Experimental Procedures). See also Figure S2.
... Experimental Timeline and Stimuli
(A) Physostigmine or placebo was administered intravenously starting 25 min prior to onset of the visuospatial attention task and concurrent MEG recording, then continuing until 15 min prior to end of experimental session.
(B) Each trial began with onset of a symbolic cue (right or left arrow, as shown) for 500 ms, indicating which hemifeld to attend. Participants fixated the central cross throughout the remainder of the trial, which comprised a 0.8–1.2 s (rectangular distribution) cue-target interval, followed by presentation of bilateral gratings for 500 ms, with up to 2.2 s for participants to make the tilt judgement (clockwise or counterclockwise relative to diagonal) for the grating in the attended hemifield.
(C) Example display of bilateral gratings, spatial **frequency** 1.2 cycles/degree, circular window of 7 degrees, centered at 8 degrees eccentricity along the horizontal meridian.

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The problem of nonlinear **oscillations** of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear **oscillations** of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced **oscillations** of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations **frequencies**. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial **oscillation** form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

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Source-reconstructed lagged coherence topographies localise the sensorimotor alpha and beta **oscillations** to the same region and dissociate them from occipital sources. Brain slices through the right (blue) and the left (green) sensorimotor cortex show that the source-reconstructed lagged coherence is able to dissociate occipital from sensorimotor sustained activity. Source-reconstructed lagged coherence topographies show the left and right sensorimotor alpha (upper row) and beta (bottom row) rhythms, separated from the occipital sources. Note that the slices in the 1st column are viewed from the front and in the 2nd column from below, such that the right and left side of the subject are displayed on the left and right side of each image, respectively. As both horizontal cross-sections look nearly identical, we only show the horizontal cross-section with the lower of the two sensorimotor sources.
... Lagged coherence as a function of **frequency** and lag evaluates the typical duration of rhythms. (A) Lagged coherence can be used to evaluate the typical time period over which the phase remains consistent, namely by expressing it as a function of the lag between the epochs that are used for estimating between-epoch phase consistency. Here, we use a signal from a posterior MEG recording site, vary the lag from 3 to 20cycles, and calculate lagged coherence at 10Hz. It can be seen that lagged coherence monotonically decreases with lag. (B) By plotting lagged coherence as a function of both lag and **frequency**, the different rhythms can be compared with respect to the time period over which the phase remains consistent. It can be seen that the alpha band lagged coherence peak (between 10 and 15Hz) remains high for much longer than the beta band lagged coherence peak (between 24 and 30Hz), indicating that in this example data the posterior alpha phase remains consistent over a much longer time period than the posterior beta phase.
... Lagged coherence measures the phase consistency between non-overlapping data fragments. (A) Raw data is cut into epochs of 3cycles of the **frequency** of interest. Here, 5 adjacent epochs are shown. In each pair of epochs, the first epoch (left of the vertical bar) is referred to as xn and the second (right of the vertical bar) as xn+1. (B) For each epoch, the Fourier coefficient F(xn)k is calculated, in which k is the index of the **frequency** of interest in the series of Fourier **frequencies**. Each Fourier coefficient is represented by a vector in the complex plane; the Fourier coefficient's amplitude corresponds to the vector's length, and its phase to the vector's angle relative to the positive horizontal axis. (C) The phase of the product F(xn)kF(xn+1)kH equals the difference between the phases of F(xn)k and F(xn+1)k. (D) The across-epoch consistency of the phase differences in C indexes rhythmicity: the more rhythmic the signal, the more consistent the phase differences. This phase consistency can be measured by the average over the epoch pairs of the products F(xn)kF(xn+1)kH in C. This average is the lagged autospectrum and is displayed in D. Note that the vectors in C and D are on the same scale. The amplitude of the lagged autospectrum denotes both the strength of the rhythmicity and the amplitude of the rhythm. The pure phase consistency across epochs is best measured by lagged coherence, which is calculated by normalising the lagged autospectrum by the average amplitude in all epochs used (see Eq. 1). This results in a value between 0 and 1, which quantifies the signal's rhythmicity (i.e. phase consistency across time).
... Neuronal **oscillations**... Scalp topographies of beta band lagged coherence, but not power, allow for the identification of the sensorimotor rhythm. (A) Beta band (20–28Hz) lagged coherence but not power allows for the identification of the putative sensorimotor sources from their scalp topographies. Power and lagged coherence were calculated for synthetic planar gradients, which have their maximum above the neuronal sources. Notice that the alpha band (7–15Hz) lagged coherence topography is dominated by the spread of the high amplitude posterior source. The arrows indicate the spatial origin of the spectra shown in B. (B) Power (grey lines) is dominated by low **frequencies** to a much larger degree than lagged coherence (black lines). The lagged coherence spectra from both the putative sensorimotor (top) and posterior recording sites (bottom) are plotted on the same scales. Note that the peak **frequencies** of rhythmicity (13 and 28Hz) are higher than those of power (10 and 20Hz).

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We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.

Data Types:

- Document

We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.

Data Types:

- Document

Data Types:

- Document

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