Neural oscillations are a ubiquitous form of neural activity seen across scales and modalities. These neural rhythms correlate with diverse cognitive functions and brain states. One mechanism for changing the oscillatory dynamics of large neuronal populations is through neuromodulator activity. An intriguing phenomenon explored here is when local neuromodulation of a distinct neuron type within a single brain nucleus exerts a powerful influence on global cortical rhythms. One approach to investigate the impact of local circuits on global rhythms is through optogenetic techniques. My first project involves the statistical analysis of electrophysiological recordings of an optogenetically-mediated Parkinsonian phenotype. Empirical studies demonstrate that Parkinsonian motor deficits correlate with the emergence of exaggerated beta frequency (15-30 Hz) oscillations throughout the cortico-basal ganglia-thalamic network. However, the mechanism of these aberrant oscillatory dynamics is not well understood. A previous modeling study predicted that cholinergic neuromodulation of medium spiny neurons in the striatum of the basal ganglia may mediate the pathologic beta rhythm. Here, this hypothesis was tested using selective optogenetic stimulation of striatal cholinergic interneurons in normal mice; stimulation robustly and reversibly amplified beta oscillations and Parkinsonian motor symptoms. The modulation of global rhythms by local networks was further studied using computational modeling in the context of intrathalamic neuromodulation. While intrathalamic vasoactive intestinal peptide (VIP) is known to cause long-lasting excitation in vitro, its in vivo dynamical effects have not been reported. Here, biophysical computational models were used to elucidate the impact of VIP on thalamocortical dynamics during sleep and propofol general anesthesia. The modeling results suggest that VIP can form robust sleep spindle oscillations and control aspects of sleep architecture through a novel homeostatic mechanism. This homeostatic mechanism would be inhibited by general anesthesia, representing a new mechanism contributing to anesthetic-induced loss of consciousness. While the previous two projects differed in their use of empirical versus theoretical methods, a challenge common to both domains is the difficulty in visualizing and analyzing large multi-dimensional datasets. A tool to mitigate these issues is introduced here: GIMBL-Vis is a Graphical Interactive Multi-dimensional extensiBLe Visualization toolbox for Matlab. This toolbox simplifies the process of exploring multi-dimensional data in Matlab by providing a graphical interface for visualization and analysis. Furthermore, it provides an extensible open platform for distributed development by the community.

Essa dissertação dedica-se ao estudo de instabilidades cinéticas em células a combustível de membrana trocadora de prótons (PEMFC, do inglês proton exchange membrane fuel cell). As PEMFC apresentam baixíssima perda por polarização quando operadas com H2. Contudo, quando o processo de produção de H2 se dá por reforma catalítica de hidrocarbonetos, CO está presente em níveis inaceitáveis para PEMFC equipada com ânodo de Pt/C. Dentre as propostas para superar esse problema, ligas bimetálicas de Pt têm se mostrado uma alternativa promissora para tornar a célula mais tolerante à CO. Além disso, é plausível que um comportamento dinâmico surja nesse tipo de sistema eletroquímico, devido à interação de fatores como transferência de massa, corrente, potencial do eletrodo e a presença de um veneno catalítico, nesse sistema o CO, que pode ser uma impureza do H2 ou um intermediário de reação (em células a combustível alimentadas diretamente com metanol, ácido fórmico ou etanol). Uma das motivações em se estudar tais instabilidades cinéticas é que uma célula a combustível operando em regime oscilatório pode resultar em um desempenho superior, uma vez que a limpeza auto-organizada da superfície previne que o ânodo seja completamente envenenado por CO. Nesse contexto, estudou-se a emergência de instabilidades cinéticas em PEMFC operando com ânodo de Pd-Pt/C ou Pd/C durante a oxidação de H2 e H2/CO, assim como em célula a combustível a metanol direto (DMFC, do inglês direct methanol fuel cell) com ânodo de Pt black. Os resultados indicaram que oscilações de potencial surgem na PEMFC durante a oxidação H2/CO sobre Pd-Pt/C assim como sobre Pd/C. Acoplando as medidas de potencial com espectrometria de massas on line na saída do ânodo, investigou-se o consumo de CO e a produção de CO2 durante as oscilações. Observou-se que as oscilações de potencial levam a variações na fração molar de CO e CO2. Adicionalmente, identificou-se oscilações de potencial em DMFC, fenômeno até então não relatado na literatura. / This dissertation deals with kinetic instabilities in proton exchange membrane fuel cells (PEMFC). PEMFCs show very small polarization losses when operating with pure H2. However, when the H2 production takes place by catalytic reforming of hydrocarbons, CO is present in the fuel stream at unacceptable levels for PEMFC equipped with a Pt/C anode. Among the possibilities to overcome this problem, bimetallic Pt alloys have proven to be a promising alternative to increase CO tolerance. Furthermore, it is plausible that a dynamic behavior emerge in such electrochemical system due to the interaction of factors like mass transfer, current, potential, and the presence of a catalyst poison, for this system CO which can be a H2 impurity or a reaction intermediate (in direct methanol/formic acid/ethanol fuel cells). One of the motivations for studying kinetic instabilities is that a fuel cell operating under oscillatory regime might result in higher performance, because the self-organized cleaning of the surface prevents the anode to be completely poisoned by CO. In this context, kinetic instabilities were studied in PEMFC operating with Pt-Pd/C or Pd/C anode during the oxidation of H2 and H2/CO mixture, as well as in direct methanol fuel cell (DMFC) with Pt black anode. It was observed the emergency of potential oscillations during the H2/CO oxidation on both catalysts, Pt-Pd/C and Pd/C. By coupling the potential measurements with on line Mass Spectrometry in the anode outlet it was investigated a variation in the concentration of CO and CO2 during oscillatory dynamic. It was found that the potential oscillations lead to variations in the molar fraction of CO and CO2. Additionally, it was observed potential oscillations in DMFC, phenomenon not previously reported in the literature.

Among various non-smooth dynamic systems, the periodically forced oscillation system with impact is perhaps the most common in engineering applications. Usually it has an oscillator with fixed or unfixed stops. The dynamics becomes complicate due to the impact against the stops. Sometimes it leads to bifurcation and even turns to chaos. Its present applications include MEMS switch device, escapement in watch movement and so on. / As a branch of mechanics, the multi-body dynamic system is well-studied. In particular, the non-smooth dynamical system attracts many researchers because of its importance and diversity. The main behaviours of such a system include contact (slip-stick motion), friction and impact. Although various models have been developed for these behaviours and their results are often satisfactory, the truth is that they are still far from completion. In the past twenty some years, various new methods have been developed. However, none of them is universally applicable. One of the difficulties is that there are a number of explicit discontinuities, such as: (a) Coulomb friction gives a discontinuous law for the forces as a function of velocities, and (b) The contact conditions give forces that are not only discontinuous in position, but also unbounded and give rise to discontinuities in the velocities. / This thesis presents a systematic study on the periodically forced oscillation system with impact. Various existing methods are discussed and compared. In particular, impulsive differential equation, Poincare map and perturbation theory are applied. Two practical cases are included: a first-order system and the Swiss lever escapement mechanism. The latter has significant engineering value as the Swiss level escapement is the key component of mechanical watch movement. The precision dynamic model has very high numerical accuracy in describing/predicting their dynamics. The research helps to optimize the design of a commercial product. The model is validated by means of experiment. / Fu, Yu. / Adviser: Du Ruxu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3745. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 137-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Yeung Yuk Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 82-85). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Historical background --- p.2 / Chapter 1.3 --- Outline of this thesis --- p.3 / Chapter 2 --- Mode classifications --- p.5 / Chapter 2.1 --- Fluid modes --- p.6 / Chapter 2.1.1 --- f mode (fundamental mode) --- p.6 / Chapter 2.1.2 --- p mode (pressure mode) --- p.7 / Chapter 2.1.3 --- g mode (gravity mode) --- p.7 / Chapter 2.2 --- w mode (spacetime mode) --- p.8 / Chapter 3 --- Oscillations of neutron stars --- p.10 / Chapter 3.1 --- The equilibrium configurations of neutron star models --- p.10 / Chapter 3.1.1 --- Newtonian stars --- p.10 / Chapter 3.1.2 --- Relativistic stars --- p.11 / Chapter 3.2 --- Perturbation of the star's equilibrium --- p.14 / Chapter 3.2.1 --- Axial perturbation equation --- p.15 / Chapter 3.2.2 --- Boundary conditions --- p.16 / Chapter 3.2.3 --- Numerical techniques --- p.16 / Chapter 3.2.4 --- The Quasinormal modes of stars --- p.18 / Chapter 4 --- Excitation and detection of QNMs --- p.20 / Chapter 4.1 --- Studies of excitation of stellar QNMs --- p.20 / Chapter 4.2 --- Detection of QNM ringing --- p.21 / Chapter 4.3 --- Parameter estimation --- p.23 / Chapter 5 --- Oscillations of realistic neutron stars --- p.28 / Chapter 5.1 --- Motivations of study --- p.28 / Chapter 5.2 --- Realistic equations of state --- p.29 / Chapter 5.3 --- Axial QNM --- p.36 / Chapter 6 --- Logarithmic perturbation method --- p.38 / Chapter 6.1 --- Introduction --- p.38 / Chapter 6.2 --- Logarithmic perturbation theory --- p.39 / Chapter 6.3 --- Evaluation of perturbation formulae --- p.42 / Chapter 6.3.1 --- The first-order perturbation --- p.42 / Chapter 6.3.2 --- The second-order perturbation --- p.47 / Chapter 6.4 --- Comparison of LPT calculations with exact results --- p.47 / Chapter 6.5 --- Discussion --- p.51 / Chapter 7 --- Scaled coordinate logarithmic perturbation method --- p.53 / Chapter 7.1 --- Rescaling of the axial perturbation equations --- p.54 / Chapter 7.1.1 --- The original axial perturbation equations --- p.55 / Chapter 7.1.2 --- The rescaled axial perturbation equations --- p.56 / Chapter 7.2 --- The formalism of SCLPT --- p.57 / Chapter 7.2.1 --- Logarithmic perturbation theory --- p.59 / Chapter 7.2.2 --- First-order perturbation --- p.63 / Chapter 7.2.3 --- Second-order perturbation --- p.65 / Chapter 7.3 --- Comparison of the perturbation calculation with the exact result --- p.67 / Chapter 7.4 --- Discussion --- p.70 / Chapter 8 --- Conclusion --- p.73 / Chapter 8.1 --- Summary --- p.73 / Chapter 8.2 --- Outlook --- p.74 / Chapter A --- Units conventions --- p.76 / Chapter B --- Numerical technique in Leaver's series --- p.77 / Chapter C --- Method of numerical derivatives --- p.80 / Bibliography --- p.82

Inner hair cells (IHCs) are the actual sensory receptors in hearing. Immature IHCs generate spontaneous calcium-dependent action potentials. Changing the characteristic of the Ca2Å signals modulates the amplitude and duration of the action potentials in these cells. These spontaneous action potential firing patterns are thought to be important for the development of the auditory system. The aim of this thesis is to gain a deeper understanding of the electrical activity and calcium signalling during development of IHCs from a mathematical point of view. A numerical bifurcation analysis is performed to delineate the relative contributions of the model parameters to the asymptotic behaviour of the model. In particular, we investigate the pattern of periodic solutions including single (normal) spiking, pseudoplateau burstings and complex solutions using two-parameter sections of the parameter space. We also demonstrate that a simplified (three-dimensional) model can generate similar dynamics as the original (four-dimensional) IHC model. This reduced model could be characterised by two fast and one slow or one fast and two slow variables depending on the parameters’ choice. Hence, the mechanisms underlying the bursting dynamics and mixed mode oscillations in the model are studied applying 1-slow/2-fast and 2-slow/1-fast analysis, respectively.

The work presented in this thesis investigates the behaviour of the Rashba semi-conductor BiTeI and of the topological insulator $\text{Bi}_2\text{Te}_3\,$ under pressure. Using Shubnikov-de Haas quantum oscillation measurements, the evolution of the Fermi surface of both materials was tracked as a function of pressure. At ambient pressure, two distinct quantum oscillation frequencies in BiTeI, corresponding to inner and outer Fermi surface orbits as a result of spin-splitting caused by the Rashba effect, were observed. Using a model Hamiltonian with a Rashba interaction term to model this system, experimental results were fitted to determine model parameters. Based on this model, carrier densities for the samples were calculated and there was good agreement with Hall effect measurements. The phase of the oscillations showed that both Fermi surfaces have a Berry phase of $\pi$ associated with them, consistent with theoretical predictions for a Rashba system. As pressure is applied, it was observed that the inner Fermi surface expands while the outer Fermi surface shrinks. Phase analysis of the oscillations showed deviations from the ambient pressure value, hinting at a topological transition. For $\text{Bi}_2\text{Te}_3\,$, we report the observation of two oscillation frequencies ($\sim 40$ T and $\sim 340$ T) at ambient pressures. Based on the angular dependence of the oscillation frequencies, phase analysis, and comparison against band structure from published ARPES results, it is deduced that the higher frequency oscillation corresponds to the surface state of $\text{Bi}_2\text{Te}_3$. Non-linear behaviour in the Hall measurement also suggests the presence of multiple bands, and a two-band model with parameters derived from quantum oscillation measurements is used to fit the experimental data. Under pressure, a slight decrease in the low field Hall coefficient and a new frequency appearing at $\sim 20$ kbar was observed. These may be signatures of a change in the Fermi surface of $\text{Bi}_2\text{Te}_3\,$ caused by an electronic topological transition.

Lau, Hoi Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 208-212). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Gravitational wave astronomy --- p.1 / Chapter 1.2 --- Stellar pulsation and gravitational radiation --- p.3 / Chapter 1.3 --- Outline --- p.5 / Chapter 2 --- Hydrostatic stellar structure --- p.8 / Chapter 2.1 --- Structural equation --- p.9 / Chapter 3 --- Finite temperature equations of state of nuclear matter --- p.13 / Chapter 3.1 --- Finite temperature ordinary nuclear matter --- p.13 / Chapter 3.2 --- Strange Quark Matter --- p.15 / Chapter 3.3 --- Equilibrium and Dynamic EOS --- p.16 / Chapter 4 --- Stellar pulsation and gravitational radiation --- p.19 / Chapter 4.1 --- Linearized theory of general relativity --- p.19 / Chapter 4.2 --- Stellar oscillation --- p.25 / Chapter 4.3 --- Quasi-normal Mode --- p.28 / Chapter 4.3.1 --- f mode --- p.29 / Chapter 4.3.2 --- p mode --- p.29 / Chapter 4.3.3 --- g mode --- p.30 / Chapter 4.3.4 --- w mode --- p.31 / Chapter 5 --- Gravitational wave spectrum of hot compact stars --- p.32 / Chapter 5.1 --- Numerical results --- p.32 / Chapter 5.1.1 --- Temperature effect on QNM --- p.32 / Chapter 5.1.2 --- Temperature effect and QS model --- p.38 / Chapter 5.1.3 --- QNM shift due to phase transition --- p.41 / Chapter 5.2 --- Summary and prospective --- p.48 / Chapter 6 --- Universality of fundamental mode and spacetime mode --- p.50 / Chapter 6.1 --- Review --- p.50 / Chapter 6.2 --- Generic proposal of universalities --- p.53 / Chapter 6.2.1 --- Moment of Inertia --- p.54 / Chapter 6.2.2 --- Gravitational wave spectrum --- p.57 / Chapter 6.3 --- Universality on moment of inertia --- p.63 / Chapter 6.4 --- Origin of universality --- p.70 / Chapter 6.4.1 --- Tolman VII model --- p.71 / Chapter 6.4.2 --- Polytropic Model --- p.76 / Chapter 6.5 --- Application of universality --- p.82 / Chapter 6.6 --- Summary --- p.89 / Chapter 7 --- Quark star properties and gravity mode oscillation --- p.92 / Chapter 7.1 --- Introduction --- p.92 / Chapter 7.2 --- g mode frequencies of quark stars --- p.94 / Chapter 7.2.1 --- Temperature profile and p mode frequency --- p.96 / Chapter 7.2.2 --- Strange quark mass and Yp mode frequency --- p.104 / Chapter 7.3 --- Summary --- p.108 / Chapter 8 --- Gravitational radiation excitation by infalling shell --- p.111 / Chapter 8.1 --- Introduction --- p.111 / Chapter 8.2 --- Formalism --- p.116 / Chapter 8.2.1 --- Connection between star and vacuum --- p.117 / Chapter 8.2.2 --- Matter source --- p.121 / Chapter 8.2.3 --- Geodesic --- p.124 / Chapter 8.2.4 --- Source of infalling dust shell --- p.126 / Chapter 8.2.5 --- Green's function --- p.127 / Chapter 8.3 --- Gravitational Wave excitation by collapsing shell --- p.130 / Chapter 8.4 --- Features of radiation --- p.138 / Chapter 8.4.1 --- Power spectrum --- p.138 / Chapter 8.4.2 --- Wave function --- p.144 / Chapter 8.4.3 --- Energy of excitation --- p.147 / Chapter 8.5 --- Non-adiabatic oscillation --- p.153 / Chapter 8.5.1 --- Mathematical Background --- p.154 / Chapter 8.5.2 --- Numerical results --- p.158 / Chapter 8.6 --- General relativistic simulation --- p.163 / Chapter 8.6.1 --- Technical briefing --- p.163 / Chapter 8.6.2 --- Numerical results --- p.166 / Chapter 8.7 --- Summary --- p.174 / Chapter 9 --- Conclusion and remarks --- p.178 / Chapter A --- Unit conversions --- p.183 / Chapter B --- Series expansion of quark star EOS --- p.185 / Chapter C --- Accuracy of simplified mode extraction scheme --- p.188 / Chapter D --- Computation of moment of inertia --- p.193 / Chapter E --- Comment of exactness of inference scheme --- p.195 / Chapter E.1 --- Precision of the mass inferred --- p.195 / Chapter E.2 --- Accuracy of universality combinations --- p.199 / Chapter F --- Calculation of sound speed --- p.202 / Chapter G --- Mode extraction of non-adiabatic oscillation --- p.204 / Bibliography --- p.208

Prefrontal cortex (PFC) is critical to behavioral flexibility and, hence, the top-down control over bottom-up sensory information. The mechanisms underlying this capacity have been hypothesized to involve the propagation of alpha/beta (8-30 Hz) oscillations via feedback connections to sensory regions. In contrast, gamma (30-160 Hz) oscillations are thought to arise as a function of bottom-up, feedforward stimulation. To test the hypothesis that such oscillatory phenomena embody such functional roles, we assessed the performance of nine monkeys on tasks of learning, categorization, and working memory concurrent with recording of local field potentials (LFPs) from PFC. The first set of tasks consisted of two classes of learning: one, explicit and, another, implicit. Explicit learning is a conscious process that demands top-down control, and in these tasks alpha/beta oscillations tracked learning. In contrast, implicit learning is an unconscious process that is automatic (i.e. bottom up), and in this task alpha/beta oscillations did not track learning. We next looked at dot-pattern categorization. In this task, category exemplars were generated by jittering the dot locations of a prototype. By chance, some of these exemplars were similar to the prototype (low distortion), and others were not (high distortion). Behaviorally, the monkeys performed well on both distortion levels. However, alpha/beta band oscillations carried more category information at high distortions, while gamma-band category information was greatest on low distortions. Overall, the greater the need for top-down control (i.e. high distortion), the greater the beta, and the lesser the need (i.e. low distortion), the greater the gamma. Finally, laminar electrodes were used to record from animals trained on working memory tasks. Each laminar probe was lowered so that its set of contacts sampled all cortical layers. During these tasks, gamma oscillations peaked in superficial layers, while alpha/beta peaked in deep layers. Moreover, these deep-layer alpha/beta oscillations entrained superficial alpha/beta, and modulated the amplitude of superficial-layer gamma oscillations. These laminar distinctions are consistent with anatomy: feedback neurons originate in deep layers and feedforward neurons in superficial layers. In summary, alpha/beta oscillations reflect top-down control and feedback connectivity, while gamma oscillations reflect bottom-up processes and feedforward connectivity.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Microfiche copy available in Archives and Barker Engineering Library. / Vita. / Ph.D.

It was shown analytically and experimentally that when the cavity losses are perturbed, the output intensity experiences an amplitude modulation or becomes a regular train of spikes, with the frequency depending on both the frequency of perturbation as well as pump power. Coupled nonlinear rate equations including the cavity perturbation term, are solved numerically by a Runga-Kutta method using experimentally-measured parameter values for Nd: Y AG laser. A continuously pumped Nd: Y AG laser was used to verify this theory.