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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 12 (1982), S. 13-30 
    ISSN: 1432-1416
    Keywords: Biological oscillators ; Phase response curves ; Dynamical system theory ; Circadian oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are(i) spatial representation of time,(ii) learning of forward dynamics and kinetics model and(iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 30 (1978), S. 147-155 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In order to perceive a visual pattern which includes several elemental pictures, the perceiver must allot his cognitive resources to suitably selected parts of the pattern and scan them in sequence. Even when the visual field is small and eye-movement is not required, such scanning is found. We called it ‘mental scanning’ and performed psychological experiments to investigate the mechanism. The tasks were to discern whether the elemental pictures in a pattern are all the same (SP) or not (DP). The per cents correct of the task were measured for various exposure durations. We defined the threshold as the exposure duration at which 75% correct answers were obtained. Our main findings are as follows. The threshold for SP is proportional to the number of picture elements, while the threshold for DP is constant. It appears that two modes of mental scanning exist. One is serial processing for SP, and the other is parallel processing for DP. We proposed a two-layered neural network model having the following characteristics. 1) Information is transmitted as two types of signals through two separate channels; one is the transient signals to the Y layer and the other is the sustained signals slowly conducted to the X layer. 2) Interactions among neurons in the Y layer are lateral inhibitory, while those in the X layer are self-excitatory and lateralinhibitory. 3) Every neuron in the Y layer sends inhibitory signals to every neuron in the X layer except one with the same receptive field. Under these conditions, the dynamics of neurons in the X layer is represented by a set of certain equations. From phase plane analysis and numerical integration, the model appears to have an ability to account for various experimental results.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 30 (1978), S. 241-248 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Many biological oscillators are stable against noise and perturbation (e.g. circadian rhythms, biochemical oscillators, pacemaker neurons, bursting neurons and neural networks with periodic outputs). The experiment of phase shifts resulting from discrete perturbation of stable biological rhythms was developed by Perkel and coworkers (Perkel et al., 1964). By these methods, they could get important insights into the entrainment behaviors of biological rhythms. Phase response curves, which are measured in these experiments, can be classified into two types. The one is the curve with one mapping degree (Type 1), and the other is that with zero mapping degree (Type 0) (Winfree, 1970). We define the phase response curve mathematically, and explain the difference between these two types by the homotopy theory. Moreover, we prove that, if a Type 0 curve is obtained at a certain magnitude of perturbation, there exists at least one lower magnitude for which the phase response curve cannot be measured. Some applications of these theoretical results are presented.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 34 (1979), S. 81-89 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract To investigate the role of electrical junctions in the nervous system, a model system consisting of two nearly identical neurons electrotonically coupled is studied. We assume that each neuron discharges a train of impulses or bursts either spontaneously or under constant stimulus via chemical synapses. It is known that not only an electric current but also chemical substances whose molecular weight is about 1000 can pass through the junction of an electrical synapse (gap junction). So, our model system is regarded as a set of non-linear oscillators coupled by diffusion, and it may be described by a system of ordinary differential equations. Neurons are excited constantly when they are stimulated by an electric current above the threshold level. Therefore, we expect Hopf bifurcation to occur at the critical magnitude of a stimulating electric current in the system of differential equations which describes the dynamics of a single neuron. Studying our model system according to the theory of Hopf bifurcation, we found regions of diffusion constants of the electrical junction which give two kinds of periodic solutions. One is the solution where two neurons oscillate in phase synchrony. The other is where two neurons oscillate 180° out of phase. In the case where one neuron is described by the BVP model, the following was found by computer simulation. When the initial difference between the phase of two neurons is small, the two neurons come to oscillate synchronously. If the initial difference is large, however, the two come to be excited alternately. The physiological implications of these results are discussed.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 57 (1987), S. 169-185 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In order to control voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: the determination of a desired trajectory in the visual coordinates, the transformation of its coordinates to the body coordinates and the generation of motor command. Based on physiological knowledge and previous models, we propose a hierarchical neural network model which accounts for the generation of motor command. In our model the association cortex provides the motor cortex with the desired trajectory in the body coordinates, where the motor command is then calculated by means of long-loop sensory feedback. Within the spinocerebellum — magnocellular red nucleus system, an internal neural model of the dynamics of the musculoskeletal system is acquired with practice, because of the heterosynaptic plasticity, while monitoring the motor command and the results of movement. Internal feedback control with this dynamical model updates the motor command by predicting a possible error of movement. Within the cerebrocerebellum — parvocellular red nucleus system, an internal neural model of the inverse-dynamics of the musculo-skeletal system is acquired while monitoring the desired trajectory and the motor command. The inverse-dynamics model substitutes for other brain regions in the complex computation of the motor command. The dynamics and the inverse-dynamics models are realized by a parallel distributed neural network, which comprises many sub-systems computing various nonlinear transformations of input signals and a neuron with heterosynaptic plasticity (that is, changes of synaptic weights are assumed proportional to a product of two kinds of synaptic inputs). Control and learning performance of the model was investigated by computer simulation, in which a robotic manipulator was used as a controlled system, with the following results: (1) Both the dynamics and the inverse-dynamics models were acquired during control of movements. (2) As motor learning proceeded, the inverse-dynamics model gradually took the place of external feedback as the main controller. Concomitantly, overall control performance became much better. (3) Once the neural network model learned to control some movement, it could control quite different and faster movements. (4) The neural netowrk model worked well even when only very limited information about the fundamental dynamical structure of the controlled system was available. Consequently, the model not only accounts for the learning and control capability of the CNS, but also provides a promising parallel-distributed control scheme for a large-scale complex object whose dynamics are only partially known.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n+1)-th iteration is a sum of the motor command in then-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in then-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Theoretical Biology 126 (1987), S. 275-288 
    ISSN: 0022-5193
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Theoretical Biology 120 (1986), S. 389-409 
    ISSN: 0022-5193
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Theoretical Biology 86 (1980), S. 547-575 
    ISSN: 0022-5193
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
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