Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

In vivo biochemical 7.0 Tesla magnetic resonance: preliminary results of dGEMRIC, zonal T2, and T2* mapping of articular cartilage

INTRODUCTION: Ultra-high-field whole-body systems (7.0 T) have a high potential for future human in vivo magnetic resonance imaging (MRI). In musculoskeletal MRI, biochemical imaging of articular cartilage may benefit, in particular. Delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) and T2 mapping have shown potential at 3.0 T. Although dGEMRIC, allows the determination of the glycosaminoglycan content of articular cartilage, T2 mapping is a promising tool for the evaluation of water and collagen content. In addition, the evaluation of zonal variation, based on tissue anisotropy, provides an indicator of the nature of cartilage ie, hyaline or hyaline-like articular cartilage.Thus, the aim of our study was to show the feasibility of in vivo dGEMRIC, and T2 and T2* relaxation measurements, at 7.0 T MRI; and to evaluate the potential of T2 and T2* measurements in an initial patient study after matrix-associated autologous chondrocyte transplantation (MACT) in the knee. MATERIALS AND METHODS: MRI was performed on a whole-body 7.0 T MR scanner using a dedicated circular polarization knee coil. The protocol consisted of an inversion recovery sequence for dGEMRIC, a multiecho spin-echo sequence for standard T2 mapping, a gradient-echo sequence for T2* mapping and a morphologic PD SPACE sequence. Twelve healthy volunteers (mean age, 26.7 +/- 3.4 years) and 4 patients (mean age, 38.0 +/- 14.0 years) were enrolled 29.5 +/- 15.1 months after MACT. For dGEMRIC, 5 healthy volunteers (mean age, 32.4 +/- 11.2 years) were included. T1 maps were calculated using a nonlinear, 2-parameter, least squares fit analysis. Using a region-of-interest analysis, mean cartilage relaxation rate was determined as T1 (0) for precontrast measurements and T1 (Gd) for postcontrast gadopentate dimeglumine [Gd-DTPA(2-)] measurements. T2 and T2* maps were obtained using a pixelwise, monoexponential, non-negative least squares fit analysis; region-of-interest analysis was carried out for deep and superficial cartilage aspects. Statistical evaluation was performed by analyses of variance. RESULTS: Mean T1 (dGEMRIC) values for healthy volunteers showed slightly different results for femoral [T1 (0): 1259 +/- 277 ms; T1 (Gd): 683 +/- 141 ms] compared with tibial cartilage [T1 (0): 1093 +/- 281 ms; T1 (Gd): 769 +/- 150 ms]. Global mean T2 relaxation for healthy volunteers showed comparable results for femoral (T2: 56.3 +/- 15.2 ms; T2*: 19.7 +/- 6.4 ms) and patellar (T2: 54.6 +/- 13.0 ms; T2*: 19.6 +/- 5.2 ms) cartilage, but lower values for tibial cartilage (T2: 43.6 +/- 8.5 ms; T2*: 16.6 +/- 5.6 ms). All healthy cartilage sites showed a significant increase from deep to superficial cartilage (P < 0.001). Within healthy cartilage sites in MACT patients, adequate values could be found for T2 (56.6 +/- 13.2 ms) and T2* (18.6 +/- 5.3 ms), which also showed a significant stratification. Within cartilage repair tissue, global mean values showed no difference, with 55.9 +/- 4.9 ms for T2 and 16.2 +/- 6.3 ms for T2*. However, zonal assessment showed only a slight and not significant increase from deep to superficial cartilage (T2: P = 0.174; T2*: P = 0.150). CONCLUSION: In vivo T1 dGEMRIC assessment in healthy cartilage, and T2 and T2* mapping in healthy and reparative articular cartilage, seems to be possible at 7.0 T MRI. For T2 and T2*, zonal variation of articular cartilage could also be evaluated at 7.0 T. This zonal assessment of deep and superficial cartilage aspects shows promising results for the differentiation of healthy and affected articular cartilage. In future studies, optimized protocol selection, and sophisticated coil technology, together with increased signal at ultra-high-field MRI, may lead to advanced biochemical cartilage imaging.

Improved cerebellar tissue classification on magnetic resonance images of brain.

PURPOSE: To develop and implement a method for improved cerebellar tissue classification on the MRI of brain by automatically isolating the cerebellum prior to segmentation. MATERIALS AND METHODS: Dual fast spin echo (FSE) and fluid attenuation inversion recovery (FLAIR) images were acquired on 18 normal volunteers on a 3 T Philips scanner. The cerebellum was isolated from the rest of the brain using a symmetric inverse consistent nonlinear registration of individual brain with the parcellated template. The cerebellum was then separated by masking the anatomical image with individual FLAIR images. Tissues in both the cerebellum and rest of the brain were separately classified using hidden Markov random field (HMRF), a parametric method, and then combined to obtain tissue classification of the whole brain. The proposed method for tissue classification on real MR brain images was evaluated subjectively by two experts. The segmentation results on Brainweb images with varying noise and intensity nonuniformity levels were quantitatively compared with the ground truth by computing the Dice similarity indices. RESULTS: The proposed method significantly improved the cerebellar tissue classification on all normal volunteers included in this study without compromising the classification in remaining part of the brain. The average similarity indices for gray matter (GM) and white matter (WM) in the cerebellum are 89.81 (+/-2.34) and 93.04 (+/-2.41), demonstrating excellent performance of the proposed methodology. CONCLUSION: The proposed method significantly improved tissue classification in the cerebellum. The GM was overestimated when segmentation was performed on the whole brain as a single object.

Symmetric inverse consistent nonlinear registration driven by mutual information.

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

Nonlinear response to ultrasound of encapsulated microbubbles

The acoustic backscatter of encapsulated gas-filled microbubbles immersed in a weak compressible liquid and irradiated by ultrasound fields of moderate to high pressure amplitudes is investigated theoretically. The problem is formulated by considering, for the viscoelastic shell of finite thickness, an isotropic hyperelastic neo-Hookean model for the elastic contribution in addition to a Newtonian viscous component. First and second harmonic scattering cross-sections have been evaluated and the quantitative influence of the driving pressure amplitude on the harmonic resonance frequencies for different initial equilibrium bubble sizes and for different encapsulating physical properties has been determined. Conditions for optimal second harmonic imaging have been also investigated and some regions in the parameters space where the second harmonic intensity is dominant over the fundamental have been identified. Results have been obtained for albumin, lipid and polymer encapsulating shells, respectively.

Effective nonlinear model of resonant tunneling nanostructures

We introduce a model of a nonlinear double-barrier structure to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where a nonlinear local field interaction is introduced to account for those inelastic scattering phenomena. Resonance peaks seen in the transmission coefficient spectra for the linear case appear shifted to higher energies depending on the magnitude of the nonlinear coupling. Our results are in good agreement with self-consistent solutions of the Schrodinger and Poisson equations. The calculation procedure is seen to be very fast, which makes our technique a good candidate for a rapid approximate analysis of these structures.

Fermi-edge singularities in linear and nonlinear ultrafast spectroscopy

We discuss Fermi-edge singularity effects on the linear and nonlinear transient response of an electron gas in a doped semiconductor. We use a bosonization scheme to describe the low-energy excitations, which allows us to compute the time and temperature dependence of the response functions. Coherent control of the energy absorption at resonance is analyzed in the linear regime. It is shown that a phase shift appears in the coherent control oscillations, which is not present in the excitonic case. The nonlinear response is calculated analytically and used to predict that four wave-mixing experiments would present a Fermi-edge singularity when the exciting energy is varied. A new dephasing mechanism is predicted in doped samples that depends linearly on temperature and is produced by the low-energy bosonic excitations in the conduction band.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Enhanced information transmission with signal-dependent noise in an array of nonlinear elements

We have investigated information transmission in an array of threshold units that have signal-dependent noise and a common input signal. We demonstrate a phenomenon similar to stochastic resonance and suprathreshold stochastic resonance with additive noise and show that information transmission can be enhanced by a nonzero level of noise. By comparing system performance to one with additive noise we also demonstrate that the information transmission of weak signals is significantly better with signal-dependent noise. Indeed, information rates are not compromised even for arbitrary small input signals. Furthermore, by an appropriate selection of parameters, we observe that the information can be made to be (almost) independent of the level of the noise, thus providing a robust method of transmitting information in the presence of noise. These result could imply that the ability of hair cells to code and transmit sensory information in biological sensory systems is not limited by the level of signal-dependent noise. © 2007 The American Physical Society.

Transfer characteristics and propagation effects of a multi-resonance ring resonator-based optical device

We describe the linear and nonlinear optical transfer characteristics of a multi-resonance device consisting of two optical ring resonators coupled one to the other and to an optical waveguide. The propagation effects displayed by the device are compared with those of a sequence of fundamental ring resonators coupled to a waveguide.

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.