Phase Invariance Research Articles

Synaptic depression in conjunction with A-current channels promote phase constancy in a rhythmic network.

In many central pattern generators, pairs of neurons maintain an approximately fixed phase despite large changes in the frequency. The mechanisms underlying phase maintenance are not clear. Previous theoretical work suggested that inhibitory synapses that show short-term depression could play a critical role in this respect. In this work we examine how the interaction between synaptic depression and the kinetics of a transient potassium (A-like) current could be advantageous for phase constancy in a rhythmic network. To demonstrate the mechanism in the context of a realistic central pattern generator, we constructed a detailed model of the crustacean pyloric circuit. The frequency of the rhythm was modified by changing the level of a ligand-activated current in one of the pyloric neurons. We examined how the time difference of firing activities between two selected neurons in this circuit is affected by synaptic depression, A-current, and a combination of the two. We tuned the parameters of the model such that with synaptic depression alone, or A-current alone, phase was not maintained between these two neurons. However, when these two components came together, they acted synergistically to maintain the phase across a wide range of cycle periods. This suggests that synaptic depression may be necessary to allow an A-current to delay a postsynaptic neuron in a frequency-dependent manner, such that phase invariance is ensured.

Nonlinear V1 responses to natural scenes revealed by neural network analysis

A key goal in the study of visual processing is to obtain a comprehensive description of the relationship between visual stimuli and neuronal responses. One way to guide the search for models is to use a general nonparametric regression algorithm, such as a neural network. We have developed a multilayer feed-forward network algorithm that can be used to characterize nonlinear stimulus-response mapping functions of neurons in primary visual cortex (area V1) using natural image stimuli. The network is capable of extracting several known V1 response properties such as: orientation and spatial frequency tuning, the spatial phase invariance of complex cells, and direction selectivity. We present details of a method for training networks and visualizing their properties. We also compare how well conventional explicit models and those developed using neural networks can predict novel responses to natural scenes.

A temporal trace and SOM-based model of complex cell development

An activity-dependent model of complex cell development is described. The learning rules are a combination of a temporal trace rule, a Hebbian rule, anda self-organizing map (SOM). They are local, unsupervised , andbiologically realistic. The only input that is assumedis spontaneous retinal wave activity. The results show complex cells with phase invariance andorientation tuning that form an organizedmap. c

A temporal trace and SOM-based model of complex cell development

An activity-dependent model of complex cell development is described. The learning rules are a combination of a temporal trace rule, a Hebbian rule, and a self-organizing map (SOM). They are local, unsupervised, and biologically realistic. The only input that is assumed is spontaneous retinal wave activity. The results show complex cells with phase invariance and orientation tuning that form an organized map.

On the possibility of simultaneous spiral and superfluid ordering in a Fermi liquid

A study is made of one of the possible forms of ordering of Fermi systems—superfluid spiral ordering, wherein not only the phase invariance of the state is broken but so are the translational invariance and the invariance with respect to spin rotations. A general method of studying superfluid spiral ordering is formulated on the basis of the Fermi-liquid approach to the consideration of superfluid states. For a one-component Fermi system we obtain the self-consistency equations for four order parameters and the temperature of the simultaneous phase transition to the superfluid and spiral states. The system of equations is investigated in the case of two nonzero order parameters. The transition temperature and the energy gap in the spectrum of elementary fermionic excitations are obtained as functions of the parameter of the spiral. The region of values of the spiral parameter in which the spiral superfluid ordering can exist is determined. The correlation function of the spins in the presence of spiral ordering is investigated.

Spot size and Guoy phase invariant telescope for auto-alignment of resonant cavities

We present both the theory and an experimental method to accurately set up a Guoy phase telescope, where both the output spot size and orthogonality condition are invariant to distance from the cavity beam waist. We demonstrate that Gaussian spot size measurements can be used as a diagnostic to determine the desired locations of split area photodetectors. The Guoy phase invariance is verified using the tilt-locking technique.

Effect of click intensity on click-evoked otoacoustic emission waveforms: implications for the origin of emissions

The rather shallow growth of click-evoked otoacoustic emissions (CEOAE) with click intensity, namely <1 dB/dB, distinguishes genuine CEOAEs from stimulus artifacts, thereby providing the rationale for the popular ‘derived nonlinear recording’ method. However, other CEOAE nonlinearities regarding phase or envelope dependence on stimulus intensity have been barely acknowledged so far. The present work used CEOAEs from 20 normal ears recorded in response to 50–86 dB peak equivalent SPL clicks. The phases of CEOAE spectral components varied considerably with click intensity (sometimes more than 120°), mostly in a monotonic manner and in such a way that in the majority of ears, phase lagged with increasing intensity. When present, synchronized spontaneous otoacoustic emissions exhibited the same behavior. In a few instances, conspicuous frequency shifts of CEOAE spectral peaks were seen. In contrast to CEOAE phases, envelopes were almost intensity-invariant. This behavior contrasts with that of basilar membrane motion at the place tuned to the stimulus frequency, as consistently disclosed by several recent publications, i.e., no phase shift and large envelope shift with stimulus intensity. It is thought that the phase invariance of basilar membrane motion implies that whatever they do, outer hair cells cannot alter the resonance frequency of the cochlear partition. If one elaborates along this line of reasoning, the large phase shift of CEOAEs with click intensity implies that CEOAEs at frequency f cannot come from the place tuned to f and that instead, they may be intermodulation distortion products produced by nonlinear interactions between spectral components of the click stimulus over a significant length of the basilar membrane.

Optical spiral waves supported by competing nonlinearities

Four-phase spiral waves are predicted to exist in a nonlinear optical cavity with competing quadratic (i.e., ${\ensuremath{\chi}}^{(2)})$ and cubic (i.e., ${\ensuremath{\chi}}^{(3)})$ nonlinearities. These spatial structures are found in the mean-field model of a doubly resonant type-II frequency-degenerate optical parametric oscillator with an intracavity ${\ensuremath{\chi}}^{(3)}$ isotropic medium. Degenerate four-wave mixing of signal and idler fields induced by the ${\ensuremath{\chi}}^{(3)}$ medium breaks the phase invariance of the down-conversion process, producing nonlinear phase locking with four possible phase states. A parametrically forced Ginzburg-Landau equation is derived to explain the existence of multiphase spiral waves.

New strategy for reconstructing partial-Fourier imaging data in functional MRI.

Most partial Fourier (PF) approaches use a low-resolution phase estimate in the reconstruction to account for non-zero phases of the image. These methods may fail when there are large phase errors, a situation commonly encountered in T(*)(2)-weighted functional MRI (fMRI). To mitigate this problem, a method was developed based on the inversion of a matrix formulated according to a phase map derived from iterative reconstruction. To make this method computationally practical for fMRI, a strategy was introduced such that the matrix inversion is performed only once for each slice in the time series, assuming that the phase map remains constant in the time series. To ensure the temporal phase invariance, physiological noise correction and global phase correction were applied to the data before the reconstruction. This method was demonstrated to be robust and efficient for fMRI. Magn Reson Med 46:1045-1048, 2001.

Spiral waves in a class of optical parametric oscillators.

The formation of three-armed rotating spiral waves is shown to occur in a spatially extended nonlinear optical system with broken phase invariance. These new spatial structures are found in the mean-field model of a class of optical parametric oscillators (3omega-->2omega+omega) in which the multistep process 2omega=omega+omega breaks the phase invariance of the down-conversion process. A parametrically-forced Ginzburg-Landau equation is derived to explain the existence of phase-armed spiral waves.

Interaction of a shear wave with a moving domain wall in an iron garnet crystal

The boundary-value problem of the interaction of a plane monochromatic shear wave with a moving Bloch wall in an iron garnet crystal is solved in the framework of the nonexchange magnetostatic approximation on the basis of the method of phase invariants for wave problems with moving boundaries. For a shear wave incident on the domain wall, the possibility of the reflectionless birefringence is demonstrated. Numerical results illustrating the resonance properties of the magnetic subsystem are presented. It is established that, at the upper bound of the reflectionless birefringence range, the interaction of the shear wave with the domain wall manifests itself as a degenerate resonance with the solution in the form of two combined antiphase, collinearly propagating shear waves of infinitely large amplitudes, which form a zero resulting field.

Spectral estimation of NMR relaxation

In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D(1), D(2), etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (omega(1), ellipsis omega(n)), corresponding to the peak maxima. Spectral estimation of NMR relaxation allows this information content to be extended to a set of (n + 1)-tuples (lambda, omega(1), ellipsis omega(n)), where lambda is the relaxation rate. Copyright 2000 Academic Press.

A recurrent network model for the phase invariance of complex cell responses

Cortical amplification is a mechanism for modifying the selectivity of neurons through recurrent interactions. Although conventionally used to enhance selectivity, cortical amplification can also broaden it, de-tuning neurons. Here we show that the spatial-phase invariance of complex cell responses in primary visual cortex can arise using recurrent amplification of feedforward input. Neurons in the model network respond like simple cells when recurrent connections are weak and complex cells when they are strong. Simple or complex cells can coexist in such a network, and they can have a range of selectivities for image characteristics such as spatial frequency.

Spatial pooling in the second-order spatial structure of cortical complex cells

We investigate what computational mechanisms give rise to the nonlinearity of complex cell responses in the primary visual cortex. Complex cells are characterized by their nonlinear spatial properties such as spatial phase invariance and nonlinear spatial additivity. We carried out network simulations to estimate the second-order Wiener-like kernels for several different models. Models with nonlinear spatial pooling of simple-cell-like linear subunits reproduce the second-order kernels in good agreement with physiologically estimated kernels, while models without the pooling mechanism fail to reproduce the kernel. The results support the cascade mechanism consisting of simple cells’ local feature extraction followed by spatial pooling.

Are cortical models really bound by the "binding problem"?

Are cortical models really bound by the "binding problem"?

Three-wave X-ray diffraction: an analysis scheme of the sensitivity in determining triplet phase invariants.

A model for analysing the phase sensitivity of the reflection coefficients of a diffracted wave in the case of three-wave X-ray diffraction is proposed. This model considers three-wave diffraction as the interference of the directly excited and the Umweg-excited diffracted waves and seems to account properly for the phase sensitivity as well as the behaviour of an involved diffracted wave as a function of the triplet phase invariant, the polarization state of the incident wave and the diffraction geometry. The practical issues for phase determination are also considered.

The atoms of vision: Cartesian or polar?

The inherent structure of the encoding in early stages of the visual system is investigated from a combined information-theoretical, psychophysical, and neurophysiological perspective. We argue that the classical modeling in terms of linear spatial filters is equivalent to the assumption of a Cartesian organization of the feature space of early vision. We show that such a linear Cartesian feature space would be suboptimal for the exploitation of the statistical redundancies of natural images since these have a radially separable probability-density function. Therefore a more efficient representation can be obtained by a nonlinear encoding that yields a feature space with polar organization. This prediction of the information-theoretical approach regarding the organization of the feature space of early vision is confirmed by our psychophysical measurements of basic discrimination capabilities for elementary Gabor patches, and the necessary nonlinear operations are shown to be closely related to cortical gain control and to the phase invariance of complex cells. Finally, we point out some striking similarities between the polar representation in visual cortex and basic image-coding strategies pursued in shape-gain vector quantization schemes.

Three-wave grazing-incidence X-ray diffraction from thin crystal surface layers: determination of triplet phase invariants.

Numerical calculation of the angular and spectral distributions of the intensities of the specularly diffracted waves in the case of three-wave grazing-incidence X-ray diffraction is carried out using the dynamical theory. The angular and spectral distributions are shown to be uniquely and continuously dependent upon the value of the triplet phase invariant. A method of determining the value of the triplet phase invariant for thin crystal surface layers is developed, based on the comparison of experimentally measured three-wave peak profiles with the profiles calculated for different values of the triplet phase invariant. An analysis scheme of the phase sensitivity of the reflection coefficients is proposed taking into account the interference of the directly excited and the 'Umweg'-excited specularly diffracted waves.

Optimizing Shake-and-Bake for proteins.

Shake-and-Bake is a direct-methods procedure which has provided ab initio solutions for protein structures containing as many as 1000 independent non-H atoms. This algorithm extends the range of conventional direct methods by repetitively, unconditionally and automatically alternating reciprocal-space phase refinement with filtering in real space to impose constraints. The application of SnB to protein-sized molecules is significantly affected by the choice made for certain critical parameters, including the number of peaks used for density modification, the choice of phase-refinement method and the number of refinement cycles. The effects of parameter variation have been studied for six protein structures, all of which are solvable by Shake-and-Bake using data at 1.1 A or higher resolution. Solvability in the resolution range 1.2-1.4 A appears to be enhanced by the presence of heavier atoms (S, Cl). Furthermore, it appears that in this range the ratio of refinement cycles and triplet phase invariants to atoms in the structure must be increased. Large structures lacking atoms of any element heavier than oxygen also require non-traditional parameter values.

Non-Abelian geometric phase, Floquet theory and periodic dynamical invariants

For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.