Model transitions in descending FLVQ.

Fuzzy learning vector quantization (FLVQ), also known as the fuzzy Kohonen clustering network, was developed to improve performance and usability of on-line hard-competitive Kohnen's vector quantization and soft-competitive self organizing map (SOM) algorithms. The FLVQ effectiveness seems to depend on the range of change of the weighting exponent m(t). In the first part of this work, extreme m(t) values (1 and 1, respectively) are employed to investigate FLVQ asymptotic behaviors. This analysis shows that when m(t) tends to either one of its extremes, FLVQ is affected by trivial vector quantization, which causes centroids collapse in the grand mean of the input data set. No analytical criterion has been found to improve the heuristic choice of the range of m(t) change. In the second part of this paper, two FLVQ and SOM classification experiments of remote sensed data are presented. In these experiments the two nets are connected in cascade to a supervised second stage, based on the delta rule. Experimental results confirm that FLVQ performance can be greatly affected by the user's definition of the range of change of the weighting exponent. Moreover, FLVQ shows instability when its traditional termination criterion is applied. Empirical recommendations are proposed for the enhancement of FLVQ robustness. Both the analytical and the experimental data reported seem to indicate that the choice of the range of m(t) change is still open to discussion and that alternative clustering neural-network approaches should be developed to pursue during training: 1) monotone reduction of the neurons' learning rate and 2) monotone reduction of the overlap among neuron receptive fields.

A study of the relationship between muscle length, tension-time area and stiffness in cat areflexic soleus.

The relationship between muscle length and both tension-time area and stiffness were studied in the isolated cat soleus muscle during tetanic isometric contraction at different stimulus rates. The results show that: The area subtending the tension curve remains constant in a range of 8-10 mm of muscle length, for stimulation frequencies between 15 and 66 Hz. The muscle stiffness, measured using different amplitude stretches, remains constant over changes in muscle length of 10 mm. The stiffness is higher for smaller stretches than for larger ones. The data therefore show an approximately constant tension-time area and no significant changes in stiffness for variations in muscle length that exceed the physiological length variations during quiet standing. These results are discussed in the context of postural mechanisms.

Simulation of post-tetanic potentiation and fatigue in muscle using a visco-elastic model.

Post-tetanic potentiation (PTP) in single motor units was simulated using a simple visco-elastic model. Single isometric twitches and unfused tetani were obtained using a wide range of physiological input rates. Values of model parameters were chosen to simulate contraction times close to those of fast and slow muscle fibers. PTP has been attributed either to i) an augmented plateau level of active state or ii) an increase in time constant of active state decay. Our results show that a prolonged decay time of active state can account for most of the experimental data obtained in amphibian and mammalian preparations. In particular, potentiation is more marked in unfused tetani than in single twitches. Moreover the model accounts for PTP even in the case of a reduction of active state plateau due to fatigue.

Slow changes and Wiener analysis of nonlinear summation in contractions in cat muscles.

With regular trains of stimuli at a high frequency, the contribution of each stimulus to the force generated over time declines from the second to about the tenth stimulus, but then begins to increase again. This late increase is referred to as tetanic potentiation in analogy with the post-tetanic potentiation of the twitch after such a period of stimulation. With regular trains of stimuli at a low frequency, a progressive decrease in the essentially unfused twitches (negative staircase) is observed in the slow soleus muscle of the cat, while a progressive increase (positive staircase) is observed for the fast plantaris muscle. The time constant for the approximately exponential changes observed is on the order of 10 s. Random trains of stimuli were applied at intermediate frequencies and analyzed in terms of general methods of analysis for nonlinear systems. Systematic decreases in the magnitude and increases in the time course of the average tension per stimulus were observed with increasing mean rates of stimulation. Similar changes were observed for short intervals between stimuli within a given random train at a constant mean rate. These changes can be described in terms of an early depression and a later facilitation described in the previous papers in this series.

Nonlinear summation of contractions in cat muscles. I. Early depression.

Nerves to fast- and slow-twitch cat muscles were stimulated with various numbers of supramaximal pulses under isometric conditions. By subtracting the force produced by j - 1 pulses from that produced by j pulses, the contribution of the j th pulse could be compared with the response to one pulse (twitch response). A less-than-linear summation (depression) was observed during the rising phase of the twitch. This depression became increasingly prominent and longer in duration with repetitive stimulation. A more-than-linear summation (facilitation) was observed during the falling phase of the twitch, which became increasingly delayed and smaller in amplitude with repetitive stimulation. The early depression could be abolished for the first few pulses by Dantrolene [1-(5-p-nitrophenyl) furfurilidene amino hydantoin sodium hydrate], which reduced Ca++ release from the sarcoplasmic reticulum. The depression was less prominent at short muscle lengths or with stimulation of single motor units. A first-order, saturable reaction such as Ca++ binding to troponin or actin binding to myosin can quantitatively account for the early depression.

Nonlinear summation of contractions in cat muscles. II. Later facilitation and stiffness changes.

The force produced by cat muscles over time with two stimuli separated by a short interval is approximately three times that produced by a twitch of cat muscles. This facilitation of force production by a second stimulus involves both increases in magnitude and duration of the contraction. Increased magnitude is relatively more important in the fast-twitch plantaris muscle, whereas increased duration is more important in the slow-twitch soleus muscle. The facilitation decays in an approximately exponential manner with the interval between stimuli, having a time constant between one and two times the twitch contraction time in different muscles. If a third stimulus is added, the greatest facilitation is seen at intervals longer than the twitch contraction time. The drug Dantrolene, which specifically reduces Ca++ release from the sarcoplasmic reticulum, eliminates the delayed peak in facilitation with three stimuli. Associated with the increases in force with one or more stimuli are increases in muscle stiffness, which can be measured with small, brief stretches and releases that do not alter the time-course of contraction. The stiffness of soleus muscle reaches a peak after the peak in force. The increasing stiffness of the muscle can considerably facilitate transmission of force generated internally, in addition to any facilitation arising from Ca++-release mechanisms.

After hyperpolarization conductance time-course and repetitive firing in a motoneurone model with early inactivation of the slow potassium conductance system.

Early inactivation of the slow potassium conductance system (GK), responsible for the spike afterhyperpolarization (AHP) in spinal alpha motoneurones, has been introduced in a motoneurone model whose GK kinetics give rise to an exponentially decaying AHP conductance. After this modification, the model displays a plateau shaped time-course of the AHP conductance and a faster shortening of the first interval during repetitive firing induced by current steps of increasing intensities. Both features increase the resemblance between the model and the motoneurone behaviour. Comparison with real motoneurones also suggests that GK inactivation may be more developed in "slow" than in "fast" motoneurones.

The stiffness of slow-twitch muscle lags behind twitch tension: implications for contractile mechanisms and behavior.

Small, square stretches were applied during contractions of soleus and plantaris muscles in the cat to measure muscle stiffness. The stiffness of the slow-twitch soleus muscle (but not of the fast plantaris muscle) reaches a maximum after the peak in twitch tension. Since the number of active bonds should be maximum before the peak in tension, we suggest that many bonds are in the rigor state during the falling phase of the twitch. The stiffness of the bonds in this state may be useful for prolonging the twitch in slow-twitch muscles and for maintaining a posture.

Saturating summation of the afterhyperpolarization conductance in spinal motoneurones: a mechanism for 'secondary range' repetitive firing.

Summation of the potassium conductance (GK) changes underlying the spike afterhyperpolarization (AHP) has been studied in cat spinal motoneurones. Cells were directly activated by one to five short current pulses at constant rate, each evoking an action potential. The analysis was restricted to cells displaying an approximately exponential decay of the AHP conductance. In these neurones the AHP conductances given by successive spikes were found to summate in a non-linear manner. This nonlinear summation seemed well described by a neurone model based on modified Hodgkin-Huxley equations. From the model equations the total AHP conductance in motoneurones could be calculated from values of GK measured experimentally at different times during the summation process. Adaptation and steady-state firing in motoneurones are assumed to be governed by summation of AHP conductance. The same model was then utilized for simulating neuronal repetitive firing in response to current steps. Such simulations were performed after substitution of the model parameters with values measured in individual motoneurones which had also been fired repetitively by intracellular injection of long-lasting current steps. The amount of adaptation and the shape and slopes of the steady-state frequency-to-current relation were found to coincide in the model and in the corresponding motoneurones.