Phase-Amplitude Relations for a Particle with a Superposition of Two Energy Levels in a Double Potential Well

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

Четырехволновое взаимодействие на фазово-амплитудных голографических решетках в фоторефрактивном пьезокристалле класса симметрии 43m

A system of coupled-wave equations for calculating the vector amplitudes of linearly polarized light waves at four-wave mixing by phase-amplitude holographic gratings in a cubic photorefractive semiconductor of an arbitrary cut belonging to the 4 ̅3m symmetry class is presented. The dependences of the intensities of the polarization components of the reversed light wave on the orientation angle for GaAs crystal of (110)-cut are calculated on the basis of the numerical solution of the system of coupled-wave equations. The obtained dependences are compared with the known theoretical and experimental data. It is shown that the best agreement between the results of theoretical modeling and experimental data at calculating the counterpropagating four-wave mixing in GaAs crystal of (110)-cut is achieved if formation of several phase-amplitude holographic gratings is allowed, and the contribution of the photoelastic and inverse piezoelectric effects are taken into account together with absorption of the crystal.

Fast Adaptive Temperature-Based Re-Optimization Strategies for On-Line Hot Spot Suppression during Locoregional Hyperthermia

Background: Experience-based adjustments in phase-amplitude settings are applied to suppress treatment limiting hot spots that occur during locoregional hyperthermia for pelvic tumors. Treatment planning could help to further optimize treatments. The aim of this research was to develop temperature-based re-optimization strategies and compare the predicted effectiveness with clinically applied protocol/experience-based steering. Methods: This study evaluated 22 hot spot suppressions in 16 cervical cancer patients (mean age 67 ± 13 year). As a first step, all potential hot spot locations were represented by a spherical region, with a user-specified diameter. For fast and robust calculations, the hot spot temperature was represented by a user-specified percentage of the voxels with the largest heating potential (HPP). Re-optimization maximized tumor T90, with constraints to suppress the hot spot and avoid any significant increase in other regions. Potential hot spot region diameter and HPP were varied and objective functions with and without penalty terms to prevent and minimize temperature increase at other potential hot spot locations were evaluated. Predicted effectiveness was compared with clinically applied steering results. Results: All strategies showed effective hot spot suppression, without affecting tumor temperatures, similar to clinical steering. To avoid the risk of inducing new hot spots, HPP should not exceed 10%. Adding a penalty term to the objective function to minimize the temperature increase at other potential hot spot locations was most effective. Re-optimization times were typically ~10 s. Conclusion: Fast on-line re-optimization to suppress treatment limiting hot spots seems feasible to match effectiveness of ~30 years clinical experience and will be further evaluated in a clinical setting.

Decreased Phase–Amplitude Coupling Between the mPFC and BLA During Exploratory Behaviour in Chronic Unpredictable Mild Stress-Induced Depression Model of Rats

Depression is a common neuropsychiatric illness observed worldwide, and reduced interest in exploration is one of its symptoms. The control of dysregulated medial prefrontal cortex (mPFC) over the basolateral amygdala (BLA) is related to depression. However, the oscillation interaction in the mPFC-BLA circuit has remained elusive. Therefore, this study used phase–amplitude coupling (PAC), which provides complicated forms of information transmission by the phase of low-frequency rhythm, modulating the amplitude of high-frequency rhythm, and has a potential application for the treatment of neurological disease. The chronic unpredictable mild stress (CUMS) was used to prepare the rat models of depression. Moreover, multichannel in vivo recording was applied to obtain the local field potentials (LFPs) of the mPFC, the BLA in rats in control, and CUMS groups, while they explored the open field. The results showed prominent coupling between the phase of theta oscillation (4–12 Hz) in the mPFC and the amplitude of high-gamma oscillation (70–120 Hz) in the BLA. Compared to the control group, this theta–gamma PAC was significantly decreased in the CUMS group, which was accompanied by the diminished exploratory behaviour. The results indicate that the coupling between the phase of theta in the mPFC and the amplitude of gamma in the BLA is involved in exploratory behaviour, and this decreased coupling may inhibit exploratory behaviour of rats exposed to CUMS.

Neural Oscillations and Networks in Processes Specific to Auditory Imagery

Auditory imagery is a cognitive process for generating sound in our mind. Despite the absence of external stimuli, neuroimaging studies have found overlapping neural activities within perception and imagery. While neuroimaging studies have revealed activities unique to auditory imagery, namely memory retrieval and mental manipulation, little is known about the functional oscillatory networks associated with these processes. Therefore, in this study, we aimed to distinguish between neural oscillations for memory retrieval and mental manipulation processes by building a novel experimental paradigm containing multiple imagery conditions with the goal of enabling the effective investigation of different oscillatory processes. We found that frontal and temporal gamma power was associated with mental manipulation, while frontotemporal delta phase coupling and delta-gamma phase-amplitude coupling were each associated with memory retrieval during auditory imagery. Moreover, we found that oscillations reflecting auditory-motor communication were associated with memory retrieval. Our results suggest the critical role of neural oscillations associated with imagery-specific processes and present evidence supporting the long-debated role of motor functions in auditory imagery. Our work thus adds dimension to the state of knowledge regarding functional networks within auditory imagery.

Modulation of dopamine tone induces frequency shifts in cortico-basal ganglia beta oscillations

AbstractΒeta oscillatory activity (human: 13–35 Hz; primate: 8–24 Hz) is pervasive within the cortex and basal ganglia. Studies in Parkinson’s disease patients and animal models suggest that beta-power increases with dopamine depletion. However, the exact relationship between oscillatory power, frequency and dopamine tone remains unclear. We recorded neural activity in the cortex and basal ganglia of healthy non-human primates while acutely and chronically up- and down-modulating dopamine levels. We assessed changes in beta oscillations in patients with Parkinson’s following acute and chronic changes in dopamine tone. Here we show beta oscillation frequency is strongly coupled with dopamine tone in both monkeys and humans. Power, coherence between single-units and local field potentials (LFP), spike-LFP phase-locking, and phase-amplitude coupling are not systematically regulated by dopamine levels. These results demonstrate that beta frequency is a key property of pathological oscillations in cortical and basal ganglia networks.