Comment on "New Methods for Old Coulomb Few-Body Problems"

In this Comment on the above mentioned paper by F. E. Harris, A. M. Frolov, and V. H. Smith, we briefly review our contributions to development of new methods for solution of the Coulomb four-body problem. We show that our research group, headed by Prof. T. K. Rebane, had a priority in using the fully correlated exponential basis for variational calculations of four-body systems. We also draw attention to the fact that our group subsequently implemented a more advanced method, which uses highly efficient exponential-trigonometric basis functions for solution of the same problem.Comment: Accepted by the International Journal of Quantum Chemistr

Analytic Evaluation of Four-Particle Integrals with Complex Parameters

The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is developed. It allows high precision variational solution of the Coulomb four-body problem in a basis of exponential-trigonometric functions of interparticle separations. Numerical results demonstrate high efficiency and versatility of the new method.Comment: 13 pages, 4 figure

Explicit integration of one problem of motion of the generalized Kowalevski top

In the problem of motion of the Kowalevski top in a double force field the 4-dimensional invariant submanifold of the phase space was pointed out by M.P.Kharlamov (Mekh. Tverd. Tela, 32, 2002). We show that the equations of motion on this manifold can be separated by the appropriate change of variables, the new variables s1, s2 being elliptic functions of time. The natural phase variables (components of the angular velocity and the direction vectors of the forces with respect to the movable basis) are expressed via s1, s2 explicitly in elementary algebraic functions.Comment: 6 page

Microtesla MRI of the human brain combined with MEG

One of the challenges in functional brain imaging is integration of complementary imaging modalities, such as magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI). MEG, which uses highly sensitive superconducting quantum interference devices (SQUIDs) to directly measure magnetic fields of neuronal currents, cannot be combined with conventional high-field MRI in a single instrument. Indirect matching of MEG and MRI data leads to significant co-registration errors. A recently proposed imaging method - SQUID-based microtesla MRI - can be naturally combined with MEG in the same system to directly provide structural maps for MEG-localized sources. It enables easy and accurate integration of MEG and MRI/fMRI, because microtesla MR images can be precisely matched to structural images provided by high-field MRI and other techniques. Here we report the first images of the human brain by microtesla MRI, together with auditory MEG (functional) data, recorded using the same seven-channel SQUID system during the same imaging session. The images were acquired at 46 microtesla measurement field with pre-polarization at 30 mT. We also estimated transverse relaxation times for different tissues at microtesla fields. Our results demonstrate feasibility and potential of human brain imaging by microtesla MRI. They also show that two new types of imaging equipment - low-cost systems for anatomical MRI of the human brain at microtesla fields, and more advanced instruments for combined functional (MEG) and structural (microtesla MRI) brain imaging - are practical.Comment: 8 pages, 5 figures - accepted by JM

Aging, rejuvenation, and memory effects in short-range Ising spin glass: Cu0.5_{0.5}Co0.5_{0.5}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Non-equilibrium aging dynamics in 3D Ising spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ GBIC has been studied by zero-field cooled (ZFC) magnetization and low frequency AC magnetic susceptibility ($f = 0.05$ Hz), where $T_{g} = 3.92 \pm 0.11$ K. The time dependence of the relaxation rate $S(t) = (1/H)$d$M_{ZFC}/$d$\ln t$ for the ZFC magnetization after the ZFC aging protocol, shows a peak at a characteristic time $t_{cr}$ near a wait time $t_{w}$ (aging behavior), corresponding to a crossover from quasi equilibrium dynamics to non-equilibrium. The time $t_{cr}$ strongly depends on $t_{w}$, temperature ($T$), magnetic field ($H$), and the temperature shift ($\Delta T$). The rejuvenation effect is observed in both $\chi^{\prime}$ and $\chi^{\prime\prime}$ under the $T$-shift and $H$-shift procedures. The memory of the specific spin configurations imprinted during the ZFC aging protocol can be recalled when the system is re-heated at a constant heating rate. The aging, rejuvenation, and memory effects observed in the present system are discussed in terms of the scaling concepts derived from numerical studies on 3D Edwards-Anderson spin glass model.Comment: 14 pages, 14 figures; Eur. Phys. J. B accepted for publicatio

Correlation between amygdala BOLD activity and frontal EEG asymmetry during real-time fMRI neurofeedback training in patients with depression

Real-time fMRI neurofeedback (rtfMRI-nf) is an emerging approach for studies and novel treatments of major depressive disorder (MDD). EEG performed simultaneously with an rtfMRI-nf procedure allows an independent evaluation of rtfMRI-nf brain modulation effects. Frontal EEG asymmetry in the alpha band is a widely used measure of emotion and motivation that shows profound changes in depression. However, it has never been directly related to simultaneously acquired fMRI data. We report the first study investigating electrophysiological correlates of the rtfMRI-nf procedure, by combining rtfMRI-nf with simultaneous and passive EEG recordings. In this pilot study, MDD patients in the experimental group (n=13) learned to upregulate BOLD activity of the left amygdala using an rtfMRI-nf during a happy emotion induction task. MDD patients in the control group (n=11) were provided with a sham rtfMRI-nf. Correlations between frontal EEG asymmetry in the upper alpha band and BOLD activity across the brain were examined. Average individual changes in frontal EEG asymmetry during the rtfMRI-nf task for the experimental group showed a significant positive correlation with the MDD patients' depression severity ratings, consistent with an inverse correlation between the depression severity and frontal EEG asymmetry at rest. Temporal correlations between frontal EEG asymmetry and BOLD activity were significantly enhanced, during the rtfMRI-nf task, for the amygdala and many regions associated with emotion regulation. Our findings demonstrate an important link between amygdala BOLD activity and frontal EEG asymmetry. Our EEG asymmetry results suggest that the rtfMRI-nf training targeting the amygdala is beneficial to MDD patients, and that alpha-asymmetry EEG-nf would be compatible with the amygdala rtfMRI-nf. Combination of the two could enhance emotion regulation training and benefit MDD patients.Comment: 28 pages, 16 figures, to appear in NeuroImage: Clinica