Biomedical subjects

M J Korenberg

Publications and source records attributed to M J Korenberg.

14 recordsLinked to original sources

PubMed1992

Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex.

Complex cells in the cat's visual cortex show nonlinearities in processing of image luminance and movement. To study mechanisms, initially we have represented the chain of neurons from retina to cortex as a black-box model. Independent information about the visual system has helped us cast this "Wiener-kernel" model into a dynamic-linear/static-nonlinear/dynamic-linear (LNL) cascade. We then use system identification techniques to define the nature of these transformations directly from responses of the neuron to a single presentation of a stimulus composed of a sequence of white-noise-modulated luminance values. The two dynamic linear filters are mainly low-pass, and the static nonlinearity is mainly of even polynomial degree. This approximate squaring function may be effected in the animal by soft-thresholding each of the linear ON- and OFF-channel signals and then summing them, which account for "ON-OFF" responses and for the squaring operation needed for computation of "motion energy", both observed in these neurons.

Animals↗

PubMed1991

Parallel cascade identification and kernel estimation for nonlinear systems.

We consider the representation and identification of nonlinear systems through the use of parallel cascades of alternating dynamic linear and static nonlinear elements. Building on the work of Palm and others, we show that any discrete-time finite-memory nonlinear system having a finite-order Volterra series representation can be exactly represented by a finite number of parallel LN cascade paths. Each LN path consists of a dynamic linear system followed by a static nonlinearity (which can be a polynomial). In particular, we provide an upper bound for the number of parallel LN paths required to represent exactly a discrete-time finite-memory Volterra functional of a given order. Next, we show how to obtain a parallel cascade representation of a nonlinear system from a single input-output record. The input is not required to be Gaussian or white, nor to have special autocorrelation properties. Next, our parallel cascade identification is applied to measure accurately the kernels of nonlinear systems (even those with lengthy memory), and to discover the significant terms to include in a nonlinear difference equation model for a system. In addition, the kernel estimation is used as a means of studying individual signals to distinguish deterministic from random behaviour, in an alternative to the use of chaotic dynamics. Finally, an alternate kernel estimation scheme is presented.

Algorithms↗

PubMed1991

Dissection of a nonlinear cascade model for sensory encoding.

Action potential encoding in the cockroach tactile spine neuron may be treated as a single-input, single-output dynamic nonlinear process, where the input is the electric current flowing across the neuronal membrane and the output is the resultant train of action potentials. The nonlinear behavior of the system may be characterized by a functional expansion method which efficiently and accurately yields similar kernels to the Wiener method. A simple nonlinear cascade consisting of sequential dynamic linear, static nonlinear, and dynamic linear components was identified and gives a good approximation to the response of the neuron to random stimulation. Next, we attempted to study the components of the cascade by the use of a drug, phentolamine, which selectively modifies the dynamic behavior of the encoder. Application of phentolamine to the neuron caused a significant change in the first dynamic linear component of the cascade without affecting the other components. The change was much larger than the variability between results obtained from individual animals. This finding has implications for the biophysical processes which are involved in the components of the cascade.

Action Potentials↗

PubMed1990

The identification of nonlinear biological systems: Wiener kernel approaches.

Detection, representation, and identification of nonlinearities in biological systems are considered. We begin by briefly but critically examining a well-known test of system nonlinearity, and point out that this test cannot be used to prove that a system is linear. We then concentrate on the representation of nonlinear systems by Wiener's orthogonal functional series, discussing its advantages, limitations, and biological applications. System identification through estimating the kernels in the functional series is considered in detail. An efficient time-domain method of correcting for coloring in inputs is examined and shown to result in significantly improved kernel estimates in a biologically realistic system.

Linear Models↗

PubMed1990

Nonlinear mechanisms for gain adaptation in locust photoreceptors.

Intracellular membrane potential responses were recorded from locust photoreceptors under two stimulus conditions: pairs of flashes to dark-adapted receptors, and white-noise modulated light at a range of background intensities from 500 to 15,000 effective photons per second. Nonlinear analysis of the input-output relationships were performed by estimating the Volterra and Wiener kernels of the system. The Volterra kernels obtained from the double-flash experiments were similar to the Wiener kernels obtained from the white-noise experiments, except for a change of time scale. The structure of the second-order kernels obtained with either method gave evidence for a gain control mechanism acting at an early stage of the cascade. Both feedforward and feedback nonlinearities could account for the observed system behavior at any one background level. The differences in amplitude between the kernels obtained at different background levels could be accounted for by an adaptation process which further decreased the gain of the system, acting on a slower time scale, also at some early stage of the cascade.

Animals↗

PubMed1989

A robust orthogonal algorithm for system identification and time-series analysis.

We describe and illustrate methods for obtaining a parsimonious sinusoidal series representation or model of biological time-series data. The methods are also used to identify nonlinear systems with unknown structure. A key aspect is a rapid search for significant terms to include in the model for the system or the time-series. For example, the methods use fast and robust orthogonal searches for significant frequencies in the time-series, and differ from conventional Fourier series analysis in several important respects. In particular, the frequencies in our resulting sinusoidal series need not be commensurate, nor integral multiples of the fundamental frequency corresponding to the record length. Freed of these restrictions, the methods produce a more economical sinusoidal series representation (than a Fourier series), finding the most significant frequencies first, and automatically determine model order. The methods are also capable of higher resolution than a conventional Fourier series analysis. In addition, the methods can cope with unequally-spaced or missing data, and are applicable to time-series corrupted by noise. Finally, we compare one of our methods with a well-known technique for resolving sinusoidal signals in noise using published data for the test time-series.

Algorithms↗

PubMed1989

An orthogonal ARMA identifier with automatic order estimation for biological modeling.

In this paper an ARMA identification algorithm is developed for modeling biological time series data. The algorithm is based on Gram-Schmidt orthogonalization of automatically selected basis functions from a specified function space. The selection criterion is based on recursive testing of potential benefit to the model of candidate functions. The candidate functions, AR and MA terms, are tested in a pair-wise search direction until a least-squares criterion is satisfied, thereby estimating the order. Additive noise is considered and the basic algorithm extended to improve performance in noise. The algorithm is also extended to systems with inaccessible inputs (signal modeling). Modeling of biological data from speech is included, and indicates good performance. The algorithm is derived from earlier work on nonlinear systems identification.

Algorithms↗

PubMed1989

Applications of fast orthogonal search: time-series analysis and resolution of signals in noise.

In this paper a technique is examined for obtaining accurate and parsimonious sinusoidal series representations of biological time-series data, and for resolving sinusoidal signals in noise. The technique operates via a fast orthogonal search method discussed in the paper, and achieves economy of representation by finding the most significant sinusoidal frequencies first, in a least squares fit sense. Another reason for the parsimony in representation is that the identified sinusoidal series model is not restricted to frequencies which are commensurate or integral multiples of the fundamental frequency corresponding to the record length. Biological applications relate to spectral analysis of noisy time-series data such as EEG, ECG, EMG, EOG, and to speech analysis. Simulations are provided to demonstrate precise detection of component frequencies and weights in short data records, coping with missing or unequally spaced data, and recovery of signals heavily contaminated with noise. The technique is also shown to be capable of higher frequency resolution than is achievable by conventional Fourier series analysis.

Algorithms↗

PubMed1989

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.

Action Potentials↗

PubMed1989

Dissection of the neuron network in the catfish inner retina. III. Interpretation of spike kernels.

1. Three independent sets of evidence have been obtained to show that similar first- and second-order light-evoked kernels are computed for the ganglion cell when the system output is taken to be either the spike train (discrete signal) or the postsynaptic potential (analog signal). In this paper we show that the similarity of postsynaptic potential (PSP) kernels and spike kernels is readily explained by assuming an underlying cascade structure for the neural information processing. The cascade structure enables spike kernels to be mathematically related very simply to the process of generating the postsynaptic potentials of ganglion cells. 2. Mathematical analysis of the cascade structure also suggests why spike kernels appear to differ slightly from PSP kernels. The relation between the two sets of kernels predicted from our analysis is substantiated here by experiment and reveals an interconnection between several of the signals measured. 3. Our experimental results, in particular, suggest that the neuronal circuitry leading from the light stimulus to the generation of ganglion cell spike discharges can be represented as follows: either a Wiener (LN) or a dynamic linear-static nonlinear-dynamic linear (LNL) structure is followed by a highly nonlinear process [static or brief-memory Hammerstein static-nonlinear dynamic-linear (NL) structure] of spike generation. Cross-correlation between the analog input and spike output enables identification of these structures.

Action Potentials↗

PubMed1988

White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches.

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.

Action Potentials↗

PubMed1988

Exact orthogonal kernel estimation from finite data records: extending Wiener's identification of nonlinear systems.

A technique is described for exact estimation of kernels in functional expansions for nonlinear systems. The technique operates by orthogonalizing over the data record and in so doing permits a wide variety of input excitation. In particular, the excitation is not limited to inputs that are white, Gaussian, or lengthy. Diagonal kernel values can be estimated, without modification, as accurately as off-diagonal values. Simulations are provided to demonstrate that the technique is more accurate than the Lee-Schetzen method with a white Gaussian input of limited duration, retaining its superiority when the system output is corrupted by noise.

Biomedical Engineering↗

PubMed1988

Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm.

A method is presented for identifying functional expansion and difference equation representations for nonlinear systems. The method relies on an orthogonal approach which does not require explicit creation of orthogonal functions. This greatly reduces computing time, so that 15-fold increases in speed of estimating kernels or difference equation coefficients are readily obtainable, compared with a previous orthogonal technique. In addition, storage requirements are considerably diminished. A wide variety of input excitation, both random and deterministic, can be used, and the method is not limited to inputs which are Gaussian, white or lengthy. A model of the peripheral auditory system is simulated to show kernel measurement is free of artifacts using the present method, in contrast to the crosscorrelation approach.

Algorithms↗

PubMed1988

White-noise analysis in visual neuroscience.

In 1827, plant biologist Robert Brown discovered what is known as Brownian motion, a class of chaos. Formal derivative of Brownian motion is Gaussian white-noise. In 1938, Norbert Wiener proposed to use the Gaussian white-noise as an input probe to identify a system by a series of orthogonal functionals known as the Wiener G-functionals. White-noise analysis is uniquely suited for studying the response dynamics of retinal neurons because (1) white-noise light stimulus is a modulation around a mean luminance, as are the natural photic inputs, and it is a highly efficient input; and (2) the analysis defines the response dynamics and can be extended to spike trains, the final output of the retina. Demonstrated here are typical examples and results from applications of white-noise analysis to a visual system.

Action Potentials↗