Relative Phase Change Research Articles

Modeling both the magnitude and phase of complex-valued fMRI data

In MRI and fMRI, images or voxel measurement are complex valued or bivariate at each time point. Recently, (Rowe, D.B., Logan, B.R., 2004. A complex way to compute fMRI activation. NeuroImage 23 (3), 1078–1092) introduced an fMRI magnitude activation model that utilized both the real and imaginary data in each voxel. This model, following traditional beliefs, specified that the phase time course were fixed unknown quantities which may be estimated voxel-by-voxel. Subsequently, (Rowe, D.B., Logan, B.R., 2005. Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model. NeuroImage 24 (2), 603–606) generalized the model to have no restrictions on the phase time course. They showed that this unrestricted phase model was mathematically equivalent to the usual magnitude-only data model including regression coefficients and voxel activation statistic but philosophically different due to it derivation from complex data. Recent findings by (Hoogenrad, F.G., Reichenbach, J.R., Haacke, E.M., Lai, S., Kuppusamy, K., Sprenger, M., 1998. In vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at .95 Tesla by measuring changes in susceptibility and velocity. Magn. Reson. Med. 39 (1), 97–107) and (Menon, R.S., 2002. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn. Reson. Med. 47 (1), 1–9) indicate that the voxel phase time course may exhibit task related changes. In this paper, a general complex fMRI activation model is introduced that describes both the magnitude and phase in complex data which can be used to specifically characterize task related change in both. Hypotheses regarding task related magnitude and/or phase changes are evaluated using derived activation statistics. It was found that the Rowe–Logan complex constant phase model strongly biases against voxels with task related phase changes and that the current very general complex linear phase model can be cast to address several different hypotheses sensitive to different magnitude/phase changes.

Partially parallel imaging with phase‐sensitive data: Increased temporal resolution for magnetic resonance temperature imaging

Magnetic resonance temperature imaging can be used to monitor the progress of thermal ablation therapies, increasing treatment efficacy and improving patient safety. High temporal resolution is important when therapies rapidly heat tissue, but many approaches to faster image acquisition compromise image resolution, slice coverage, or phase sensitivity. Partially parallel imaging techniques offer the potential for improved temporal resolution without forcing such concessions. Although these techniques perturb image phase, relative phase changes between dynamically acquired phase-sensitive images, such as those acquired for MR temperature imaging, can be reliably measured through partially parallel imaging techniques using reconstruction filters that remain constant across the series. Partially parallel and non-accelerated phase-difference-sensitive data can be obtained through arrays of surface coils using this method. Average phase differences measured through partially parallel and fully Fourier encoded images are virtually identical, while phase noise increases with g(sqrt)L as in standard partially parallel image acquisitions..

Encoding and Retrieval During Bimanual Rhythmic Coordination.

In 2 experiments, bimanual 1:1 rhythmic coordination was performed concurrently with encoding or retrieval of word lists. Effects of divided attention (DA) on coordination were indexed by changes in mean relative phase and recurrence measures of shared activity between the 2 limbs. Effects of DA on memory were indexed by deficits in recall relative to baseline. For DA at both encoding and retrieval, the equilibrium values of relative phase were shifted and the degree of shared activity between left and right rhythmic motions was reduced. Recall was reduced, however, only for DA at encoding. The results corroborate and extend those obtained with more conventional secondary tasks (e.g., visual reaction time), suggesting attention dissimilarities between episodic encoding and retrieval.

High-Pressure Ammonia Adsorption and Dissociation on Clean Fe(111) and Oxygen-Precovered Fe(111) Studied by Sum Frequency Generation Vibrational Spectroscopy

The adsorption of gases N2, H2, O2, and NH3 that play a role in ammonia synthesis have been studied on the Fe(111) crystal surface by Sum Frequency Generation (SFG) vibrational spectroscopy using an integrated ultrahigh vacuum/high-pressure system. SFG spectra are presented for the dissociation intermediates, NH2 ( approximately 3325 cm-1) and NH ( approximately 3235 cm-1) under high pressure of ammonia (200 Torr) on the clean Fe(111) surface. Addition of 0.5 Torr of oxygen to 200 Torr of ammonia does not significantly change the bonding of dissociation intermediates to the surface. However, it leads to a phase change of nearly 180 degrees between the resonant and nonresonant second-order nonlinear susceptibility of the surface, demonstrated as a reversal of the SFG spectral features. Heating the surface in the presence of 200 Torr of ammonia and 0.5 Torr of oxygen reduces the oxygen coverage, which can be seen from the SFG spectra as another relative phase change of 180 degrees . The reduction of the oxide is also supported by Auger electron spectroscopy. The result suggests that the phase change of the spectral features could serve as a sensitive indicator of the chemical environment of the adsorbates. Clean Fe(111) is found to have a large SFG nonresonant signal. The magnitude of the nonresonant signal was dependent on the adsorption species; O2 and N2 decrease, while H2 and NH3 increase the SFG nonresonant signal. The change in nonresonant signal is correlated to the change in work function for Fe(111) upon adsorption. Adsorption-induced changes in the SFG nonresonant signal was used as an indicator of surface conditions and to monitor surface reactions.

Relative Phase Change During Quantum Operations

Quantum operations represented by completely positive maps encompass many physical processes and have been very powerful in describing quantum computation and information processing tasks. We introduce the notion of relative phase change for a quantum system undergoing a quantum operation. We find that the relative phase shift of a system not only depends on the initial state of the system, but also depends on the initial state of an ancilla with which it might have interacted in the past. The relative phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a “memory” to a quantum channel. Also the notion of relative phase shift helps us to define what we call “in-phase quantum channels.” We will present the relative phase shifts for a qubit undergoing both a depolarizing channel and complete randomization, and discuss their implications. PACS: 03.65.Vf; 03.67.-a; 03.65.Yz

Robust altitude estimation for over-the-horizon radar using a state-space multipath fading model

In previous work, a matched-field estimate of aircraft altitude from multiple over-the-horizon (OTH) radar dwells was presented. This approach exploits the altitude dependence of direct and surface reflected returns off the aircraft and the relative phase changes of these micro-multipath arrivals across radar dwells. Since this previous approach assumed high dwell-to-dwell predictability, it has been found to be sensitive to mismatch between modeled versus observed micro-multipath phase and amplitude changes from dwell-to-dwell. A generalized matched-field altitude estimate is presented here based on a state-space model that accounts for random ionospheric and target-motion effects that degrade the dwell-to-dwell predictability of target returns. The new formulation results in an efficient, robust recursive maximum likelihood (ML) estimation of aircraft altitude. Simulations suggest that the proposed technique can achieve accuracy within 5,000 ft of the true aircraft altitude, even with relatively high levels of uncertainty in modeling of dwell-to-dwell changes in the target return. A real data result is also presented to illustrate the technique.

Temporal coherence sensitivity in auditory cortex.

Natural sounds often contain energy over a broad spectral range and consequently overlap in frequency when they occur simultaneously; however, such sounds under normal circumstances can be distinguished perceptually (e.g., the cocktail party effect). Sound components arising from different sources have distinct (i.e., incoherent) modulations, and incoherence appears to be one important cue used by the auditory system to segregate sounds into separately perceived acoustic objects. Here we show that, in the primary auditory cortex of awake marmoset monkeys, many neurons responsive to amplitude- or frequency-modulated tones at a particular carrier frequency [the characteristic frequency (CF)] also demonstrate sensitivity to the relative modulation phase between two otherwise identically modulated tones: one at CF and one at a different carrier frequency. Changes in relative modulation phase reflect alterations in temporal coherence between the two tones, and the most common neuronal response was found to be a maximum of suppression for the coherent condition. Coherence sensitivity was generally found in a narrow frequency range in the inhibitory portions of the frequency response areas (FRA), indicating that only some off-CF neuronal inputs into these cortical neurons interact with on-CF inputs on the same time scales. Over the population of neurons studied, carrier frequencies showing coherence sensitivity were found to coincide with the carrier frequencies of inhibition, implying that inhibitory inputs create the effect. The lack of strong coherence-induced facilitation also supports this interpretation. Coherence sensitivity was found to be greatest for modulation frequencies of 16-128 Hz, which is higher than the phase-locking capability of most cortical neurons, implying that subcortical neurons could play a role in the phenomenon. Collectively, these results reveal that auditory cortical neurons receive some off-CF inputs temporally matched and some temporally unmatched to the on-CF input(s) and respond in a fashion that could be utilized by the auditory system to segregate natural sounds containing similar spectral components (such as vocalizations from multiple conspecifics) based on stimulus coherence.

Spatial organization in Europe of decadal and interdecadal fluctuations in annual rainfall

AbstractThe spatial patterns of decadal and bidecadal fluctuations in annual rainfall in Europe are identified. Filtering of time series of the anomaly in annual rainfall is carried out using the Morlet wavelet technique. Reconstruction is achieved by summing the contributions from bands of wavelet time scales; the decadal band and the bidecadal band are composed of contributions from the bands of the (10 to 17 year) and (17 to 27 year) time scales respectively. Results indicate that (1) the spatial organization of the decadal and bidecadal components of annual rainfall are standing‐wave‐like organized patterns. Three standing decadal fluctuations zonally aligned formed the spatial pattern from 1900 until 1931; thereafter the pattern changed into a NW–SE orientation. The decadal band shows an average 12 year period. (2) The spatial organization of the bidecadal component was composed of three standing fluctuations from 1903 to 1986. After 1987, two standing bidecadal fluctuations were located over Europe. The orientation of the bidecadal fluctuations changed during the period under study. Until 1913 the spatial pattern of the bidecadal component was zonally aligned. Since 1913 and until 1986 the three bidecadal fluctuations composing the spatial pattern were aligned SW–NE; starting in 1987, the spatial pattern is composed of two standing fluctuations zonally aligned. The bidecadal spatial pattern shows an average period of 20 to 22 years in length. (3) At the decadal and bidecadal time scales, the first principal component of the spatial field of anomaly in annual rainfall and the North Atlantic oscillation (NAO) index are connected. The upper positive third (lower negative third) of values of the first principal component are indicative of an extensive area with positive (negative) anomalies in annual rainfall. (4) At the decadal time scale the relative phase between the first principal component and the NAO index changes through the period under study; these changes define three regimes. (i) During the regime covering the period 1900 (start of period under study) to about 1945, at the time of peak values in decadal NAO index there takes place a transition between extremes (a neutral state) of the decadal rainfall spatial pattern (first principal component takes small absolute values). In addition, for a positive (negative) peak value of NAO index the spatial pattern of annual rainfall evolves toward an area of predominantly positive (negative) anomalies. (ii) The second regime starts about 1946 and continues to the early 1980s. At the time of the negative (positive) peak in decadal NAO there is a prevailing spatial pattern of positive (negative) anomalies of decadal rainfall. (iii) The third regime starts around the late 1970s and continues to the end of the period under study (in 1996). There is a change of relative phase within this period in the late 1980s. In this regime a spatial pattern of prevailing positive or negative anomaly of decadal rainfall takes place during values of decadal NAO close to zero. (5) At the bidecadal time scale the relative phase between the first principal component and the NAO index remains almost constant through the period under study. The first principal component of the transformed bidecadal component of annual rainfall anomalies attains its positive (negative) peak about 3 years before the bidecadal component of NAO reaches its negative (positive) peak. Copyright © 2002 Royal Meteorological Society.

Off-diagonal geometric phases.

We investigate the adiabatic evolution of a set of nondegenerate eigenstates of a parametrized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.

Helicopter Vibration Reduction through Cyclic Variations in Rotor Blade Root Stiffness

This study analytically examines the influence of cyclic variations in flap-, lag-, and torsion-stiffness of the blade root region (at harmonics of the rotational speed), for reduction of vibratory hub loads of a helicopter in forward flight. The results indicate that considerable reduction in hub vibrations is possible using small-to-moderate amplitude cyclic variations in stiffness (no greater than 15% of the baseline stiffness value). Torsion stiffness variations produced moderate reductions in vertical hub force, lag stiffness variations produced substantial reductions in all hub forces and the hub yaw moment, and flap stiffness variations produced very significant reductions in all hub forces and the hub roll and pitch moments. The amplitude of the cyclic stiffness variations required generally increase with increasing forward speed, for comparable reductions in vibration. At any given forward speed, if the amplitudes of cyclic stiffness variation are too large, the hub vibrations can actually increase. The stiffness variations that reduce the vibratory hub loads could produce increases in certain vibratory blade root load harmonics. Vibration reductions are achieved due to a decrease in the inertial contribution to the hub loads, or a change in relative phase of various contributions.

Eigenvectors of a raman medium

We show the existence of discrete sets of Raman sidebands which self-consistently establish a Raman coherence and propagate without change in amplitude and relative phase. Equivalently, there exist periodic femtosecond-time-scale, temporal pulse shapes which propagate without change in shape.

Comparative analysis of gait in Parkinson's disease, cerebellar ataxia and subcortical arteriosclerotic encephalopathy

Movement coordination, transition and stability aspects of gait in individuals with Parkinson's disease were investigated. Changes in movement coordination were evaluated by means of relative phase changes between upper and lower extremities and stability of patterns by means of the standard deviation of relative phase. Spectroscopic analysis of individual limb oscillators and of the relative phase between these oscillators was used to assess the contribution of lower and higher (e.g., tremor) frequency components on the coordination dynamics. Coordination changes in five patients and five age-matched controls were evaluated by means of accelerometry while movement velocity was manipulated as a control parameter on a motor-driven treadmill. Relative phase changes and stability features showed gradual changes in upper and lower extremity oscillations with walking velocity, a finding consistent with model predictions by Schöner et al. (1990) regarding gait changes in the quadrupedal walking mode. Parkinson's disease patients showed overall less adaptations in relative phase than the control group, especially those involving the upper extremities. Frequency analyses of relative phase also demonstrated that 1.(a) systematic scaling of walking velocity can affect the dominant frequency of Parkinsonian tremor,2.(b) higher order frequency components in relative phase can play a functional, stabilizing role, and3.(c) 1/ƒ scaling properties of the relative phase power spectrum can identify the higher degree of constraint on the coordination dynamics in Parkinson's disease.

Bayesian Approach to Guidance in the Presence of Glint

When tracking targets with radar, changes in target aspect with respect to the observer can cause the apparent centerofradarree ectionstowandersignie cantly. Theresulting noisy angleerrorsarecalledtargetglint. Glintmay severely affect the tracking accuracy, particularly when tracking largetargetsat shortranges (such as might occur in the e nal homing phase of a missile engagement ). The effect of glint is to produce heavy-tailed, time-correlated non-Gaussiandisturbancesontheobservations.ItiswellknownthattheperformanceoftheKalmane lterdegrades severely in the presence of such disturbances. We propose a random-sample-based implementation of a Bayesian recursive e lter. Thise lteris based on the Metropolis ‐Hastings algorithm and theGaussian sum approach. The key advantage of the e lter is that any nonlinear/non-Gaussian system and/or measurement models can be routinely implemented. Tracking performance of the e lter is demonstrated in the presence of glint. I. Introduction G LINTis dee nedasthe inherentcomponent oferrorin aradar’ s measurement of position or Doppler frequency of a complex target due to interference of the ree ections from different elements of the target. A complex target, such as an aircraft or tank, may be considered as being made up of a number of independent scattering elements. The radar return from such a target is the vector sum of the radar returns from each of the individual scatterers. As the relative position of the radar and the scatterers changes, the relative phase of the radar returns varies, causing large e uctuations in the combined signal. The change in relative phase of the signal returns causes a change in the apparent target center and, hence,the angular error measured by the radar. This angular noise or scintillation is called glint. Glint can cause the apparent location of the target to fall outside of its physical span (this can be simply demonstrated by analysis of a two-source target ). The linear displacement of the apparent target position due to glint varies inversely with range. As a rough guide, the standard deviation of the angular glint from an aircraft target is about kL/R, where L is the wing span of the target, R istherangetothetarget,and k isaconstanttakingavaluebetween 0.1 and 0.2 (Ref. 1). Glint is particularly troublesome for target tracking because it is a low-frequency effect, the bandwidth of the error typically being a few hertz. In Ref. 2, the correlation time tgc of the glint noise is shown to be approximately tgc o ¸ 3:4!aL

Identification of axial rigidity during locomotion in parkinson disease

Objectives: To identify coordination changes and stability in the movements of the trunk during locomotion in Parkinson disease (PD) as a function of walking velocity. Study Design: Comparison of treadmill locomotion with an opto-electronic tracking device. Patients: Newly diagnosed patients with PD ( n = 27) and a group of healthy control subjects ( n = 11). Results: Coordination between transversal pelvic and thoracic rotations showed significantly smaller changes in mean relative phase ( p < .0001) and lower variability in relative phase ( p < .0001) in the PD group. No significant differences were found in stride duration and variability in stride duration. Conclusions: The relative phase data contradict traditional notions of increased variability in motor control in PD and pinpoint the importance of the trunk in identifying axial rigidity. This discrepancy may be due to lack of control for walking velocity in earlier studies. It is concluded that systematic manipulation of walking velocity can identify coordination deficits and rigidity in trunk movement. This coordination of trunk movement can also be a sensitive measure for (early) diagnosis and the assessment of movement and pharmacological therapy in PD.

Signal coherence and energy effects of propagating internal solitary wave packets

Order-400 Hz sound propagated through continental-shelf internal solitary wave packets is shown by simulation to fluctuate strongly via mode coupling. The coupling is controlled by the modal input conditions, wave and packet dimensions, and the ambient sound-speed profile. In the case of a moving packet, relative modal phase changes dominate over the others, changing the coupling and controlling signal fluctuations. The phasing within the packet varies over minutes in a moving packet, causing fluctuations with comparable time scales. The directionality of energy flux between high-order acoustic modes and (less attenuated) low-order modes determines a gain factor for distantly detected signals. A significant finding is that a packet near a source will amplify low-order modes if the source favors high-order modes, giving amplification at distant ranges. Conversely, a packet far from a source can energize otherwise quiet higher modes. Intermittency in the coupling means that signal energy fluctuations and modal diversity fluctuations at a distant receiver are complementary, with energy fluctuations suggesting a source-region packet and mode fluctuations suggesting a receiver-region packet. In addition to the monochromatic results described above, the effects on pulses (broadband signals) will be compared with experimental observations. [Work supported by ONR Ocean Acoustics.]

Effects of phase shifts on four-beam interference patterns

An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.

Waveguide Zeeman interferometry for thin-film chemicalsensors

A chemical sensor is demonstrated which is based on Si{sub 3}N{sub 4} optical waveguides coated with species-selective thin films and using Zeeman interferometry as the detection technique. Relative phase change between TE and TM modes is measured. Real time and reversible response to toluene is shown with ppm level sensitivity.

Unambiguous phase determination using a new X-ray interferometer on separated crystals

A new X-ray interferometer for phase-sensitive diffractometry is considered. The method exploits measurements of relative phase changes in a standing wave between two separated crystals. Analysis of the superposition of the minimal-phase profile retrieved via a logarithmic Hilbert transform and unknown phase term allows the determination of the complete phase profile.

Self-organization of trajectory formation. I. Experimental evidence.

Most studies examining the stability and change of patterns in biological coordination have focused on identifying generic bifurcation mechanisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescent degrees of freedom (df) are spontaneously recruited and active df suppressed. To examine such behavior, in part I we study a single limb system composed of three joints (wrist, elbow, and shoulder) performing the kinematically redundant task of tracing a sequence of two-dimensional arcs of monotonically varying curvature, kappa. Arcs were displayed on a computer screen in a decreasing and increasing kappa sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted to flexion-extension of the wrist, elbow, and shoulder. Only a few coordinative patterns among the three joints were stably produced, e.g., in-phase (flexion-extension of one joint coordinated with flexion-extension of another joint) and antiphase (flexion-extension coordinated with extension-flexion). As kappa was systematically increased and decreased, switching between relative phase patterns was observed around critical curvature values, kappa c. A serendipitous finding was a strong 2:1 frequency ratio between the shoulder and elbow that occurred across all curvature values for some subjects, regardless of the wrist-elbow relative phase pattern. Transitions from 1:1 to 2:1 frequency entrainment and vice versa were also observed. The results indicate that both amplitude modulation and relative phase change are utilized to stabilize the end-effector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators, in which the relative phases (phi) between the components and the relative joint amplitudes (rho) are treated as collective variables with arc curvature as a control parameter.

Field line resonant pulsations associated with a strong dayside ionospheric shear convection flow reversal

We discuss a set of coordinated observations from the arrays of Greenland ground magnetometers, Sondrestrom incoherent scatter radar, and the DMSP, GOES 7, and IMP 8 satellites during 1000–1400 UT on August 4, 1991. The work presented here follows work presented by Clauer and Ridley [1995]. In the previous work we show that this particular interval is characterized by a large positive interplanetary magnetic field (IMF) By and near‐zero IMF Bz components. Associated with these conditions is a very strong ionospheric convection shear reversal boundary in the dayside noon and prenoon sector in the northern hemisphere. The convection reversal boundary is observed to be very dynamic, showing wave‐like displacements of several degrees in invariant latitude with a tailward phase propagation. These variations are associated with magnetic pulsations with a period of about 34 min. We have suggested that these waves are produced by a Kelvin‐Helmholtz instability at the shear convection reversal boundary. We present here a more detailed analysis of the magnetic variations from the Greenland arrays of magnetometers. Our new findings show that equatorward of the convection reversal boundary, there is power in the pulsation spectra in bands with periods of about 34, 17, 12, and 8 min. Examination of the northward component of the pulsations along a meridional chain of stations ranging from 76.23° to 66.86° invariant latitude shows high coherence between stations and a change in relative phase of about 160° over the observed latitude range for the 8‐min. pulsations. These observations are consistent with the expected signature of a field line resonance. We suggest that the source of the resonance is the disturbance generated at the shear convection reversal boundary which then produces resonances on nearby, equatorward closed field lines. In this case we suggest that the source is the Kelvin‐Helmholtz wave established at the east‐west convection shear which develops near local noon and prenoon regions during large IMF By positive conditions. This is possibly the first observation of the field line resonance associated with such a source.