The Quantum Scattering Limit for a Regularized Wigner Equation

The oscillatory potentials (OPs) of the electroretinogram (ERG) identify the high frequency wavelets which are seen riding on the top of the ascending limb of the b-wave. Despite the refinement in ERG recording techniques, which now allow for a more selective amplification of the OPs, their clinical utility still remains somewhat limited. Furthermore, while it has long been recognized that the different OPs which builds a given response are generated by distinct retinal events, amplitudes of clinically recorded oscillatory potentials are still reported using the artificial variable 'sum of OPs (SOPs)' which represent the sum amplitude of all the OPs identified in a given response; a method which is prone to compromise the diagnostic possibilities of the oscillatory potential response. The purpose of this report is to present a method of analysis of the OP response which is based on the relative amplitude of each OP. For the sake of clarity this report will focus on the analysis of the suprathreshold photopic OP response evoked the flash for 8.9 cd-m-2-sec in energy delivered against a rod desensitizing background of 30 cd-m-2 in luminance. The amplitude of each of the three major OPs (ie: OP2, OP3 and OP4) that normally compose this response was reported in relative units (ie: OP chi/SOPs) a method shown to minimize intersubject variability and at the same time allow for each OP to be evaluated individually. With the above method I have reviewed 289 clinical OP responses collected during a 7 year interval and identified more than 10 different categories of responses of which 6 were shown to demonstrate specific anomalies for one or two OPs. The selectivity and reproducibility of my observation were confirmed on follow-up testings as well as in pedigree studies. Use of this method of OP analysis should significantly increase the clinical utility of the oscillatory potentials and also facilitate comparisons between clinical laboratories.

We obtain the bound-state solutions of the radial Schr\"odinger equation (SE) with the shifted Deng-Fan (sDF) oscillator potential in the frame of the Nikiforov-Uvarov (NU) method and employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding wave functions are obtained in closed form for arbitrary -state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

Approximation of Cauchy-type singular integrals with high frequency Fourier kernel

In isolated segments of the 16- to 20-day old chick embryo, increasing the Mg2+ concentration from 1.3 to 5.0 mmoles/liter in the superfusate caused complete suppression of spontaneous rhythmic activity that appeared as synchronous cyclical oscillations of electrotonic potentials in the dorsal and ventral roots. A similar change was recorded when the Ca2+ concentration was decreased from 2.6 to 1.0 mmole/liter, but in this case tonic discharges of impulses (spikes) could occur. Further, during the disappearance of the spontaneous activity due to changing the concentration of Ca2+ or Mg2+, in six out of eight experiments another type of rhythmic activity was seen, appearing as oscillations of electrotonic potentials in the ventral roots that were independent of oscillations in the dorsal roots. The amplitude of these oscillations of potential in the ventral roots was up to 200 µV, and their duration was up to 400 msec. The highest frequency of this activity was 0.4 sec−1. The possible functional significance of the observed patterns of activity is discussed.

We consider the hydrogen atom $\mathrm{H}(1s)$ exposed to an ultrashort laser pulse with a central frequency ${\ensuremath{\omega}}_{0}$ ranging from several hundreds of eV to 1.5 keV ($\ensuremath{\approx}55$ a.u.) and a peak intensity of $3.51\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{4pt}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$. We study the excitation of the atom by stimulated Raman scattering, a process involving pairs of frequencies (${\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2}$). These frequencies are non-negligible components of the pulse Fourier transform and they satisfy the condition ${E}_{g}+\ensuremath{\hbar}{\ensuremath{\omega}}_{1}={E}_{b}+\ensuremath{\hbar}{\ensuremath{\omega}}_{2},{E}_{g}$ and ${E}_{b}\ensuremath{\equiv}{E}_{n}$ being the ground-state and the excited-state energy, respectively. The numerical results obtained by integrating the time-dependent Schr\odinger equation (TDSE) are compared with calculations in lowest order perturbation theory (LOPT). In LOPT we consider, in the second order of PT, the contribution of the term $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ in the dipole approximation and, in first order of PT, the expression of ${\mathbf{A}}^{2}$ taken for first-order retardation effects. ($\mathbf{A}$ denotes the vector potential of the field and $\mathbf{P}$ is the momentum operator.) We focus on the Raman excitation of bound states with principal quantum numbers $n$ up to $n=13$. The evaluation in perturbation theory of the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution to $1s\ensuremath{-}ns$ and $1s\ensuremath{-}nd$ transition probabilities uses analytic expressions of the corresponding Kramers--Heisenberg matrix elements. At fixed pulse duration $\ensuremath{\tau}=6\ensuremath{\pi}$ a.u. ($\ensuremath{\approx}0.48$ fs), we find that the retardation effects play an important role at high frequencies: they progressively diminish as the frequency decreases until the contribution of $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ dominates over the ${\mathbf{A}}^{2}$ contribution for ${\ensuremath{\omega}}_{0}$ values of a few a.u. We also study the dependence of the Raman process on the pulse duration for several values of ${\ensuremath{\omega}}_{0}$. In the case ${\ensuremath{\omega}}_{0}=13\phantom{\rule{4pt}{0ex}}\mathrm{a}.\mathrm{u}.\phantom{\rule{4pt}{0ex}}(\ensuremath{\approx}354\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ where dipole and nondipole contributions are of the same order of magnitude, we present the Raman excitation probability as a function of the pulse duration for excited $ns,\phantom{\rule{4pt}{0ex}}np$, and $nd$ states.

The harmonic-generation (HG) spectra of the ${\mathrm{H}}_{2}^{+}$ molecular ion generated by short, intense, linearly polarized laser pulses are calculated nonperturbatively by solving a three-dimensional time-dependent Schr\"odinger equation. It is found that while ${\mathrm{H}}_{2}^{+}$ radiates in a similar manner to an atomic system such as H or ${\mathrm{He}}^{+}$ at high frequencies, the molecular ion in high-vibrational states or at large internuclear distances behaves analogously to a two-level system in an intense, relatively-long-wavelength laser field. It will be shown that symmetric molecular ions should in general produce more efficient harmonic generation than atoms, due to the presence of molecular charge-resonance (CR) states, which have no atomic analogues. Two HG plateaus, one molecular due to CR transitions and one atomiclike, appear for a long-wavelength excitation. Each plateau has its own maximum harmonic-number cutoff, which can be rationalized in terms of the maximum energy which can be acquired by an electron in the laser field.

Brief optogenetic stimulation of thalamocortical axons evoked a 400 Hz wavelet, 'ripplet,' in the extracellular field potential in cortical layer 4, together with phase-locked spike bursts in fast-spiking inhibitory interneurons and alternating excitatory and inhibitory synaptic currents in excitatory cells.

Oscillation potential in strychninized olfactory bulb.

Image Deblurring is an ill-posed inverse problem used to reconstruct the sharp image from the unknown blurred image. This process involves restoration of high frequency information from the blurred image. It includes a learning technique which initially focuses on the main edges of the image and then gradually takes details into account. As blind image deblurring is ill-posed, it has infinite number of solutions leading to an ill-conditioned blur operator. So regularization or prior knowledge on both the unknown image and the blur operator is needed to address this problem. The performance of this optimization problem depends on the regularization parameter and the iteration number. In already existing methods the iterations have to be manually stopped. In this paper, a new idea is proposed to regulate the number of iterations and the regularization parameter automatically. The proposed criteria yields, on average, an ISNR only 0.38dB below what is obtained by manual stopping. The results obtained with synthetically blurred images are good and considerable, even when the blur operator is ill-conditioned and the blurred image is noisy.

A large body of evidence has shown that sharp wave ripples (SWRs), highly synchronized oscillations of the local field potential (LFP) in the CA1 pyramidal layer of the hippocampus, play a prominent role in memory consolidation. SWRs typically occur in periods of non-REM sleep, but have also been observed during awake rest periods of animals engaged in cognitive tasks. These events have been observed in rodents, non-human primates, and humans, suggesting they are evolutionarily conserved and contribute to memory formation. Numerous neurological diseases and insults, including traumatic brain injury (TBI), impair learning and memory. Mild TBI (mTBI) is the most prevalent form of TBI, and can cause memory impairments that, in some cases, last for months-to-years. Clinical and experimental studies have shown that these impairments can occur in the absence of visible physical damage to the hippocampus. In the present study, we examined whether an mTBI alters the properties of SWRs in rodents. Seven days after a mild fluid percussion injury (mFPI), recording electrodes were implanted into the CA1 subfield of the hippocampus of sham and injured rats. After seven days of recovery, LFPs and the activity of CA1 neurons were simultaneously recorded. Recordings were carried out when animals were exploring an arena containing two objects, one of which was moved between recording sessions. This allowed us to evaluate how changes in the environment affected SWR incidence and properties. Our data show that compared to uninjured controls, mFPI rats had reduced numbers of SWR events. Of the SWRs recorded, those from mTBI rats had shorter durations, reduced power, and higher frequencies than those in control animals. We also found that the modulation of the activity of CA1 pyramidal neurons by SWRs was markedly impaired in mTBI animals. Taken together, our data indicate that mTBI alters the electrophysiological properties of SWRs and reduces the synchronization of pyramidal neuron activity to SWRs. These electrophysiological changes may have implications in mTBI-associated memory impairments.

Abnormal oscillatory activity in the basal ganglia is increasingly implicated in the pathophysiology of Parkinson's disease. Such activity is recorded in patients in the form of oscillations in the local field potential (LFP) picked up in the subthalamic nucleus. Previous studies have focused on correlations between features of the time averaged power or amplitude spectrum of the LFP and the clinical state, either off medication or in response to levodopa. However, average spectral densities do not take account of time variant spectral properties and we hypothesised that these dynamic properties of the spectrum of the LFP would contain additional information about clinical state. Here we assess the variability in LFP amplitude over time using the coefficient of variation (CV), evaluating this with regard to clinical state off medication and in response to levodopa in two datasets. The CV of activity in the high beta frequency band was found to be correlated with clinical state off levodopa (rho=−0.59, p<0.001) and this was shown to be complementary, rather than redundant, to spectral amplitude in a multiple regression analysis, selective for rigidity–bradykinesia and highly focal. Similarly, a strong correlation was found between change in clinical scores and change in high beta CV following levodopa (rho=−0.66, p=0.004). This too was selective for rigidity–bradykinesia and non-redundant to spectral power in a multiple regression model. Our results indicate that temporal stability in the beta band is correlated with rigidity–bradykinesia. It is suggested that loss of beta reactivity is deleterious to basal ganglia function over and above any concomitant change in absolute level of beta synchrony. The CV of LFP beta band amplitude may potentially provide an additional index of clinical state suitable for feedback control in closed loop stimulation therapy.

Electrochemical oscillations during the oxidation of 2-(dimethylamino)ethanethiol

Power electronic converters are typical nonlinear systems in frequency domain. With a perturbation frequency excitation, the current and voltage of power converters in steady state contain not only perturbation but also many sidebands. In a Microgrid containing a large amount of power converters, one converter's switching frequency ripples are other converters' perturbations and beat frequency components will be generated if switching frequencies of those power converters are different. As the control loops always take high gains in low frequency regions and the low pass filters almost have no effect on low-frequency disturbances, if the beat frequency component has certain values, they may be magnified and presented as oscillations. This paper develops a frequency domain model to describe the characteristics of power converter around switching frequency range and to analyze the high frequency interactions of power converters in Micorgrid. The voltage mode controlled boost converters are illustrated as demonstration. The proposed model indicates that switching frequency affects the output characteristics of power converters significantly. In a system consists of two boost converters in parallel, the beat frequency oscillation that traditional output impedance models fail to explain could be accurately predicted by the proposed model. In addition, based on this model, design guideline is proposed to avoid the potential beat frequency oscillation in parallel system. Simulation results validate the accuracy and effectiveness of the proposed method.

An explicitly-sparse representation for oscillatory kernels with wave atom-like functions

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N-dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.