Analysis of Dynamic Brain Imaging Data

Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this paper we develop appropriate techniques of analysis and visualization of such imaging data, in order to separate the signal from the noise, as well as to characterize the signal. The techniques developed fall into the general category of multivariate time series analysis, and in particular we extensively use the multitaper framework of spectral analysis. We develop specific protocols for the analysis of fMRI, optical imaging and MEG data, and illustrate the techniques by applications to real data sets generated by these imaging modalities. In general, the analysis protocols involve two distinct stages: `noise' characterization and suppression, and `signal' characterization and visualization. An important general conclusion of our study is the utility of a frequency-based representation, with short, moving analysis windows to account for non-stationarity in the data. Of particular note are (a) the development of a decomposition technique (`space-frequency singular value decomposition') that is shown to be a useful means of characterizing the image data, and (b) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files. Originally submitted to the neuro-sys archive which was never publicly announced (was 9804003

Diffusion of wave packets in a Markov random potential

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.Comment: 19 pages, acknowledgments added and typos correcte

Field-induced long-range order in the S=1 antiferromagnetic chain

The quasi-one dimensional S=1 antiferromagnet in magnetic field H is investigated with the exact diagonalization of finite chains and the mean field approximation for the interchain interaction. In the presence of the single-ion anisotropy D, the full phase diagram in the $HT$ plane is presented for H \parallel D and H \perp D. The shape of the field-induced long-range ordered phase is revealed to be quite different between the two cases, as observed in the recent experiment of NDMAP. The estimated ratio of the interchain and intrachain couplings of NDMAP (J'/J ~ 10^{-3}) is consistent with the neutron scattering measurement.Comment: 4 pages, Revtex, with 6 eps figure

Field induced long-range-ordering in an S=1 quasi-one-dimensional Heisenberg antiferromagnet

We have measured the heat capacity and magnetization of the spin one one-dimensional Heisenberg antiferromagnet NDMAP and constructed a magnetic field versus temperature phase diagram. We found a field induced long-range magnetic ordering. We have been successful in explaining the phase diagram theoretically.Comment: 6 pages, 18 figure

Schrodinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrodinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication

Haldane-gap excitations in the low-H_c 1-dimensional quantum antiferromagnet NDMAP

Inelastic neutron scattering on deuterated single-crystal samples is used to study Haldane-gap excitations in the new S=1 one-dimensional quantum antiferromagnet NDMAP, that was recently recognized as an ideal model system for high-field studies. The Haldane gap energies $\Delta_x=0.42$ meV, $\Delta_y=0.52$ meV and $\Delta_z=1.86$ meV, for excitations polarized along the a, b, and c crystallographic axes, respectively, are directly measured. The dispersion perpendicular to the chain axis c is studied, and extremely weak inter-chain coupling constants $J_y=1.8\cdot 10^{-3}$ meV and $J_x=3.5\cdot 10^{-4}$ meV, along the a and b axes, respectively, are determined. The results are discussed in the context of future experiments in high magnetic fields.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

High Magnetic Field ESR in the Haldane Spin Chains NENP and NINO

We present electron spin resonance experiments in the one-dimensional antiferromagnetic S=1 spin chains NENP and NINO in pulsed magnetic fields up to 50T. The measured field dependence of the quantum energy gap for B||b is analyzed using the exact diagonalization method and the density matrix renormalization group method (DMRG). A staggered anisotropy term (-1)^i d(S_i^x S_i^z + S_i^z S_i^x) was considered for the first time in addition to a staggered field term (-1)^i S_i^x B_st. We show that the spin dynamics in high magnetic fields strongly depends on the orthorhombic anisotropy E.Comment: 4 pages, RevTeX, 4 figure