Analysis and simulation of networks of mutually inhibiting neurons

Morishita, Iwao; Yajima, Akio

doi:10.1007/bf00270672

Cited by 59 publications

(13 citation statements)

References 11 publications

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“…In Matsuoka's model, the activity of each neuron is modeled by a simple continuous-variable neuron model originally developed by Morishita and Yajima (1972). An input S i 7 to the system increases the membrane potential x i .…”

Section: Two/two Hypothesismentioning

confidence: 99%

Modeling discrete and rhythmic movements through motor primitives: a review

Dégallier

Ijspeert

2010

Biol Cybern

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Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet, an increasing interest for a comprehensive model for movement generation requires to bridge the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movement within the framework of motor primitives, i.e. of modular generation of movements. Thereby we hope to get an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed relatively to biological concepts such as force fields and central pattern generators and are then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes this work.

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Section: Two/two Hypothesismentioning

confidence: 99%

Modeling discrete and rhythmic movements through motor primitives: a review

Dégallier

Ijspeert

2010

Biol Cybern

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“…At the next step in the auditory process, an instantaneous sigmoidal non-linearity R is applied, followed by a low pass filter with impulse response h. These operations model the threshold and saturation that occur in the hair cell channels and the leakage of electrical current throughout the membranes of these cells [14], [12]. The resulting cochlear output,…”

Section: Sigmoidal Operationmentioning

confidence: 99%

“…One processing model, the lateral inhibitory network (LIN), has been closely studied with a view to extracting the spectral pattern of the acoustic stimulus [14], [13], [15]; and we shall implement it in our alogorithm. Scientifically, it reasonably reflects proximate frequency channel behavior, and mathematically it is relatively simple.…”

Section: Lateral Inhibitory Networkmentioning

confidence: 99%

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Intrinsic wavelet and frame applications

Benedetto

Andrews

2011

SPIE Proceedings

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There are intrinsic wavelet applications, by which we mean mathematical modeling of a physical phenomenon in which wavelet theory is the most natural quantitative means of explaining the phenomenon. This is not the same as the invaluable use of dyadic wavelets, say, as a tool with which to zoom-in or -out with regard to multi-scale phenomena. An example of an intrinsic wavelet application is wavelet auditory modeling (WAM). WAM is analyzed herein, and a natural excursion, one of many possibilities, is taken from WAM to applications of finite frames. This path includes the role of the Discrete Fourier Transform (DFT) in WAM, the emergence of DFT frames, and their use in analyzing Σ∆ quantization, which itself is a staple in audio engineering as well as in a host of other applications.

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“…At the next step in the auditory process, an instantaneous sigmoidal nonlinearity R is applied, followed by a low pass filter with impulse response h. These operations model the threshold and saturation that occur in the hair cell channels and the leakage of electrical current throughout the membranes of these cells [34,39]. The resulting cochlear output, where "0" denotes composition of functions and where convolution * is with respect to time, is a planar auditory nerve pattern sent to the brain.…”

Section: Sigmoidal Operationmentioning

confidence: 99%

Frames, Irregular Sampling, and a Wavelet Auditory Model

Benedetto

Scott

2001

Nonuniform Sampling

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14A Wavelet Auditory Model (WAM) is constructed in tenns of wavelet frames and an irregular sampling algorithm for Fourier frames. Its theoretical effectiveness is demonstrated in the context of speech coding, and its original fonnulation is found in [8][9]. The presentation of WAM in this chapter emphasizes its underlying mathematical ideas, and, in particular, develops the notions from the theory of frames and irregular sampling that arise naturally in constructing WAM. IntroductionWe shall develop some of the basic theory of frames, as well as conse-, quences ofthat theory from the area of irregular sampling. Moreover, we shall see how these ideas playa natural role in modelling parts of the mammalian auditory process with the purpose of using this process to devise signal reconstruction algorithms in the field of speech coding.The theory of frames is due to Duffin and Schaeffer [22], and it was developed to address problems in non-harmonic Fourier series. Prior to [22], these problems were concerned with finding criteria on real sequences {tn} so that the closed linear span, span{e t }, of exponentials e t (f) = e'2rtjtnf would be equal to the space L2 [-0, 0] offinit~ energy signals defin~d on [-0, 0]. The origins of

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Analysis and simulation of networks of mutually inhibiting neurons

Cited by 59 publications

References 11 publications

Modeling discrete and rhythmic movements through motor primitives: a review

Modeling discrete and rhythmic movements through motor primitives: a review

Intrinsic wavelet and frame applications

Frames, Irregular Sampling, and a Wavelet Auditory Model

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