Nonlinear Encoding Research Articles

Double average parallel steady‐state free precession imaging: Optimized eddy current and transient oscillation compensation

Balanced steady-state free precession (SSFP) imaging is sensitive to off-resonance effects, which can lead to considerable artifacts during a transient phase following magnetization preparation or steady-state interruption. In addition, nonlinear k-space encoding is required if contrast-relevant k-space regions need to be acquired at specific delays following magnetization preparation or for transient artifact reduction in cardiac-gated k-space segmented CINE imaging. Such trajectories are problematic for balanced SSFP imaging due to nonconstant eddy current effects and resulting disruption of the steady state. In this work, a novel acquisition strategy for balanced SSFP imaging is presented that utilizes scan time reduction by parallel imaging for optimized "double average" eddy current compensation and artifact reduction during the transient phase following steady-state storage and magnetization preparation. Double average parallel SSFP imaging was applied to k-space segmented CINE SSFP tagging as well as nongated centrically encoded SSFP imaging. Phantom and human studies exhibit substantial reduction in steady-state storage and eddy current artifacts while maintaining spatial resolution, signal-to-noise ratio, and similar total scan time of a standard SSFP acquisition. The proposed technique can easily be extended to other acquisition schemes that would benefit from nonlinear reordering schemes and/or rely on interruption of the balanced SSFP steady state.

Nonlinear encoding of tactile patterns in the barrel cortex.

Cells in the rodent barrel cortex respond to vibrissa deflection with a brief excitatory component and a longer suppressive component. The response to a given deflection is thus scaled because of suppression induced by a preceding deflection, causing the neuronal response to be linked to the temporal properties of the peripheral stimulus. A paired-deflection stimulus was used to characterize the postexcitatory suppression and a 3-deflection stimulus was used to investigate the nonlinear response to patterns of whisker deflections in barbiturate-anesthetized Sprague-Dawley rats. The postexcitatory suppression was not dependent on a sensory-evoked action potential to the first deflection, implying that it is likely a subthreshold property of the network. The suppression induced by a deflection served to suppress both the excitatory and suppressive components of a subsequent neuronal response, thus effectively disinhibiting it. Two different response properties were observed in the recorded cells. Approximately 65% responded to a vibrissa deflection with an excitatory component followed by a suppressive component and 35% responded with excitation, suppression, and a subsequent rebound in excitation. Based on these observations of postexcitatory dynamics, a prediction method was used to estimate neuronal responses to more complex stimulus trains. Using the 2nd-order representation obtained from the paired-deflection stimulus, responses to general periodic deflection patterns were well predicted. A higher cutoff frequency was predicted for rebound cells compared with cells not exhibiting rebound excitation, consistent with experimental observations. The method also predicted the response of neurons to a random aperiodic deflection pattern. Therefore the temporal structure of cortical dynamics after a single deflection dictates the response to complex temporal patterns, which are more representative of stimuli encountered under natural conditions.

ChemSpaceShuttle: A tool for data mining in drug discovery by classification, projection, and 3D visualization

AbstractThe ChemSpaceShuttle toolbox provides a graphical interface allowing for ligand‐based design of focused compound libraries by means of linear and non‐linear projection techniques and clustering algorithms. The software implements a non‐linear encoder network and non‐linear partial least squares for the projection of high‐dimensional descriptor vectors into a three dimensional space for visualisation. Compound clustering by a self‐organising map (SOM) is incorporated. Visualization can facilitate the selection of compounds with desired properties from large compound libraries. Two sample applications are presented: similarity‐based compound selection for focused library design, and classification of drugs and nondrugs. A version of ChemSpaceShuttle is freely available at URL: http://gecco.org.chemie.uni‐frankfurt.de/gecco.html.

Convergence properties of three spike-triggered analysis techniques

We analyse the convergence properties of three spike-triggered data analysis techniques. Our results are obtained in the setting of a probabilistic linear–nonlinear (LN) cascade neural encoding model; this model has recently become popular in the study of the neural coding of natural signals. We start by giving exact rate-of-convergence results for the common spike-triggered average technique. Next, we analyse a spike-triggered covariance method, variants of which have been recently exploited successfully by Bialek, Simoncelli and colleagues. Unfortunately, the conditions that guarantee that these two estimators will converge to the correct parameters are typically not satisfied by natural signal data. Therefore, we introduce an estimator for the LN model parameters which is designed to converge under general conditions to the correct model. We derive the rate of convergence of this estimator, provide an algorithm for its computation and demonstrate its application to simulated data as well as physiological data from the primary motor cortex of awake behaving monkeys. We also give lower bounds on the convergence rate of any possible LN estimator. Our results should prove useful in the study of the neural coding of high-dimensional natural signals.1http://www.cns.nycu/edu/∼liam2A brief summary of some of the results presented here is to appear in the NIPS02 Conference Proceedings (Paninski 2002).

A nonlinear encoder in crayfish sustaining fibers

The properties of the voltage to spike train encoder in crayfish visual interneurons are characterized with steps and sine waves of current and illumination. Impulse trains elicited by current steps exhibit rapid adaptation and encoder adaptation contributes to a rate sensitive frequency response in which the gain increases with stimulus frequency and the impulse rate modulation phase leads the current. Similar results obtain in the relation between impulse rate modulation and the synaptic potential. We conclude that encoder adaptation is the basis of the encoder's high sensitivity to voltage transients and describe the relevance of both the transient sensitivity and the tonic discharge at synapses made by the same neurons.

Independent factor analysis.

We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a two-step procedure. In the first step, the source densities, mixing matrix, and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectation-maximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of gaussians; thus, all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear estimator. A variational approximation of this algorithm is derived for cases with a large number of sources, where the exact algorithm becomes intractable. Our IFA algorithm reduces to the one for ordinary FA when the sources become gaussian, and to an EM algorithm for PCA in the zero-noise limit. We derive an additional EM algorithm specifically for noiseless IFA. This algorithm is shown to be superior to ICA since it can learn arbitrary source densities from the data. Beyond blind separation, IFA can be used for modeling multidimensional data by a highly constrained mixture of gaussians and as a tool for nonlinear signal encoding.

Responses to transients in living and simulated neurons

This paper is concerned with synaptic coding when inputs to a neuron change over time. Experiments were performed on a living and simulated embodiment of a prototypical inhibitory synapse. These were used to test a simple model composed of a fixed delay preceding a nonlinear encoder. Based on these results, we present a qualitative model for phenomena previously observed in the living preparation, including hysteresis and dependence of discharge regularity on rate of change of presynaptic spike rate. As change is the rule rather than the exception in nature, understanding neurons responses to nonstationarity is essential for understanding their function.

Linear and Nonlinear Encoding Properties of an Identified Mechanoreceptor on the Fly Wing Measured with Mechanical Noise Stimuli

ABSTRACT The wing blades of most flies contain a small set of distal campaniform sensilla, mechanoreceptors that respond to deformations of the cuticle. This paper describes a method of analysis based upon mechanical noise stimuli which is used to quantify the encoding properties of one of these sensilla (the d-HCV cell) on the wing of the blowfly Calliphora vomitoria (L.). The neurone is modelled as two components, a linear filter that accounts for the frequency response and phase characteristics of the cell, followed by a static nonlinearity that limits the spike discharge to a narrow portion of the stimulus cycle. The model is successful in predicting the response of campaniform neurones to arbitrary stimuli, and provides a convenient method for quantifying the encoding properties of the sensilla. The d-HCV neurone is only broadly frequency tuned, but its maximal response near 150 Hz corresponds to the wingbeat frequency of Calliphora. In the range of frequencies likely to be encountered during flight, the d-HCV neurone fires a single phase-locked action potential for each stimulus cycle. The phase lag of the cell decreases linearly with increasing frequency such that the absolute delay between stimulus and response remains nearly constant. Thus, during flight the neurone is capable of firing one precisely timed action potential during each wingbeat, and might be used to modulate motor activity that requires afferent input on a cycle-by-cycle basis.

Comparison of Encoding Properties of Campaniform Sensilla on the Fly Wing

ABSTRACTThe wing blade of the blowfly Calliphora vomitoria (L.) carries an array of campaniform sensilla which have previously been divided into slowly and rapidly adapting classes based on their responses to step indentations. In the present study, the physiological characteristics of six sensilla of these two classes are examined within a 20–400 Hz frequency range, using a noise analysis that quantifies linear and nonlinear encoding properties. Both classes exhibit a broad response maximum near 150 Hz, corresponding to the typical wingbeat frequency of the blowfly, and display rectification, limiting the spike response to a narrow portion of a stimulus cycle. The similarity in the encoding properties between the two groups is largely a consequence of the high wingbeat frequency of flies, which precludes any individual neurone from acting as a magnitude detector. Instead, during flight the campaniform neurones might act as ‘one-shot’ detectors, firing a single action potential at a precise phase of each wing stroke cycle. An array of such detectors would be capable of monitoring the passage of a deformational wave as it travels along the wing during each wingbeat.

P.c.m. nonlinear counting encoder

Companded encoders of high resolution, such as may be required for p.c.m. transmission of high-quality sound-programme signals, can be realised using the ‘counting’ principle. In the reported implementation, a reference waveform of ramps of different slopes are generated by integrating the output from a d.a. convenor.

Logarithmic PCM Encoding Without Diode Compandor

Instantaneous companding is a useful technique for the improvement of the transmission quality of PCM systems. In this paper various nonlinear encoding and decoding techniques without using diode compandors are stated with a focus on the logarithmic decoders, which are composed of cascaded attenuators. Hyperbolic sinusoidal law is also derived from the logarithmic law and is obtained by an attenuation line decoder. These nonlinear laws are attained on the attenuation-linear basis. Likewise, various passive decoders on the immittance-linear basis can be considered. In this case the nonlinear law is expressed by a rational function of the digital variable x . Also a decoder based on the multinomial expansion is introduced, whose nonlinear law is given by a polynomial of x . It is shown that the hyperbolic sine curve provides more uniform signal-to-noise characteristics for some range of the mean speech volume, while the modified hyperbolic law yields as high signal-to-noise ratio as is obtained by the exponential law without great loss in the signal-to-noise ratio for louder speech. A few experimental studies of these decoders are described.

Logarithmic PCM encoding without diode compandor

Instantaneous companding is a useful technique for the improvement of the transmission quality of PCM systems. In this paper various nonlinear encoding and decoding techniques without using diode compandors are stated with a focus on the logarithmic decoders, which are composed of cascaded attenuators. Hyperbolic sinusoidal law is also derived from the logarithmic law and is obtained by an attenuation line decoder. These nonlinear laws are attained on the attenuation-linear basis. Likewise, various passive decoders on the immittance-linear basis can be considered. In this case the nonlinear law is expressed by a rational function of the digital variable x . Also a decoder based on the multinomial expansion is introduced, whose nonlinear law is given by a polynomial of x . It is shown that the hyperbolic sine curve provides more uniform signal-to-noise characteristics for some range of the mean speech volume, while the modified hyperbolic law yields as high signal-to-noise ratio as is obtained by the exponential law without great loss in the signal-to-noise ratio for louder speech. A few experimental studies of these decoders are described.

A survey of telephone speech-signal statistics and their significance in the choice of a p.c.m. companding law

Published information concerning the mean speech volume and likely range of volumes in a telephone circuit is summarized, and curves are reproduced for the variation in instantaneous amplitude of an individual talker. It is concluded that, to be able to handle both types of variation, a p.c.m. system should have its smallest quantization step at least 62dB below the peak limiting level. This range can be handled by a 7-digit binary code using non-linear encoding (companding). Two main types of non-linear characteristic, namely logarithmic and hyperbolic, are compared, first on the basis of signal/quantizing-noise ratio and secondly in terms of theoretical information content. It is shown that, provided that the non-linearity parameter is chosen to give an adequate dynamic range, there is little to choose between the two characteristics. The possibility of using automatic volume regulators to reduce the dynamic range is also considered, but it is concluded that they give little advantage.

On optimum non-linear extraction and coding filters

The problem of determining optimal non-linear least-square filters is solved for a class of stationary time series. This theory is then used as the basis for developing a band-width reduction scheme using non-linear encoding and decoding filters, for the same class of signals. A simple illustrative example is included.