Browsing by Subject "Oscillations"
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Item Oscillation criteria of the Hille type for ordinary differential equations(Texas Tech University, 1970-08) Walker, Billy KennethNot availableItem Response of a nonlinear two-degree-of-freedom system to a horizontal harmonic excitation(Texas Tech University, 1985-12) Li, WenlungAn elastic structure containing a fluid subjected to a horizontal sinusoidal excitation is investigated. The system is found to include cubic nonlinearities. The system response is determined by using the multiple scales asymptotic approximation method. The method predicts that primary resonances may occur when the excitation frequency, Ω is close to either the first mode natural frequency, ω1, or the second mode natural frequency, ω2. The system behavior under the fourth order internal resonance condition (ω2 ≈ 3ω1) is predicted. The system response under conditions of primary resonances (Ω ≈ω1 and Ω≈ω2), together with internal resonance is also considered. Other features, such as amplitude jump phenomenon and chaotic-like response have been observed. Two possible responses have been found when Ω is near ω2 = unlmodal response and autoparametric interaction response. The boundaries of these two motions are defined in the excitation amplitude - frequency plane. Moreover, the so called "static attractor" is also observed.Item Theta-frequency oscillatory synchrony in the dendrites of hippocampal CA1 pyramdial neurons(2013-05) Vaidya, Sachin Prashant; Johnston, Daniel, 1947-A CA1 pyramidal neuron in the rodent hippocampus integrates inputs from as many as 30,000 synapses distributed over hundreds of microns, making synaptic integration an intricate spatio-temporal computation. Crucial to this computation, is the timing of synaptic inputs at the axo-somatic integration site. Consequently, it would be beneficial if co-incident proximal and distal inputs arrive simultaneously at the axo-somatic integration site. This, however, is a challenge considering that spatially dispersed inputs have to propagate varying distances, leading to location-dependent temporal differences at the soma. Here we show that CA1 pyramidal neurons have an intrinsic biophysical mechanism in the form of a gradient of HCN channels that actively counteracts location-dependent temporal differences of dendritic inputs at the soma. HCN channels, due to their slow kinetics and unusual gating properties, impart an inductive reactance to the neuronal membrane properties. Using multi-site whole cell recordings, we show that this gradient of inductive reactance actively compensates for the location-dependent capacitive delay of dendritic inputs. This leads to a response synchrony of spatially dispersed inputs at the soma. This response synchrony is optimum for oscillatory signals in the theta frequency range (4-12 Hz). Using computational modeling we show that the characteristic sigmoidal distribution of HCN channels in CA1 neurons is crucial for the efficient and exclusive transfer of these synchronous theta frequencies from dendrite to the soma. To understand the significance of this oscillatory synchrony during synaptic integration, we used the dynamic clamp technique to simulate different temporal patterns of synaptic input in the dendrites of CA1 neurons. Our results reveal that this oscillatory synchrony is best harnessed by theta and gamma (40-140 Hz) frequency synaptic input patterns in CA1 neurons. Gamma and theta oscillations are associated with synchronizing activity across space in the hippocampal network. Our results thus identify a novel mechanism by which this synchrony extends to activity within single pyramidal neurons with complex dendritic arbors.