Evidence for different nonlinear summation schemes for lines and gratings at threshold

Within a wide class of multichannel models of the visual system it is suggested that spatial distributions of luminance are processed by the independent activation of grating detectors, or spatial frequency channels. Probability summation is often described in terms of Quick's nonlinear pooling model [Quick RF (1974) Kybernetik 16:65–67]. Using this model, we find evidence for the existence of different kinds of nonlinear summation at threshold; for compound gratings with well-separated spatial frequency components, the threshold functions indicate nonlinear summation which is not compatible with probability summation, while for line patterns well separated in the spatial domain the probability summation rule proves compatible with the data. Received: 24 June 1998 / Accepted in revised form: 16 March 1999     

A mathematical model of the adaptive control of human arm motions

This paper discusses similarities between models of adaptive motor control suggested by recent experiments with human and animal subjects, and the structure of a new control law derived mathematically from nonlinear stability theory. In both models, the control actions required to track a specified trajectory are adaptively assembled from a large collection of simple computational elements. By adaptively recombining these elements, the controllers develop complex internal models which are used to compensate for the effects of externally imposed forces or changes in the physical properties of the system. On a motor learning task involving planar, multi-joint arm motions, the simulated performance of the mathematical model is shown to be qualitatively similar to observed human performance, suggesting that the model captures some of the interesting features of the dynamics of low-level motor adaptation. Received: 20 September 1994 / Accepted in revised form: 18 November 1998     

Self-organization of trajectory formation

 Most studies examining the stability and change of patterns in biological coordination have focused on identifying generic bifurcation mechanisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescent degrees of freedom (df ) are spontaneously recruited and active df suppressed. To examine such behavior, in part I we study a single limb system composed of three joints (wrist, elbow, and shoulder) performing the kinematically redundant task of tracing a sequence of two-dimensional arcs of monotonically varying curvature, κ. Arcs were displayed on a computer screen in a decreasing and increasing κ sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted to flexion-extension of the wrist, elbow, and shoulder. Only a few coordinative patterns among the three joints were stably produced, e.g., in-phase (flexion-extension of one joint coordinated with flexion-extension of another joint) and antiphase (flexion-extension coordinated with extension-flexion). As κ was systematically increased and decreased, switching between relative phase patterns was observed around critical curvature values, κ_c. A serendipitous finding was a strong 2:1 frequency ratio between the shoulder and elbow that occurred across all curvature values for some subjects, regardless of the wrist-elbow relative phase pattern. Transitions from 1:1 to 2:1 frequency entrainment and vice versa were also observed. The results indicate that both amplitude modulation and relative phase change are utilized to stabilize the end-effector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators, in which the relative phases (φ) between the components and the relative joint amplitudes (ρ) are treated as collective variables with arc curvature as a control parameter. Received: 2 February 1996/Accepted in revised form: 13 December 1996     

Reconstruction of equilibrium trajectories during whole-body movements

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions (`Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis. Received: 3 March 1997 / Accepted in revised form: 2 November 1998     

A distributed control model for the air-righting reflex of a cat

A multisegment, multijoint model of a falling animal is presented to examine the effectiveness of a two-stage control scheme in a zero-momentum self-righting maneuver. The model contains a much larger number of degrees of freedom than is required to execute a self-righting maneuver and is thus capable of providing multiple solutions for the same task. The decentralized control scheme is designed to achieve gross turning in minimum time and to maintain a steady orientation relative to gravity after the turn has been achieved. The scheme is able to determine the sequence of steps necessary to execute the motor task and also incorporates learning features. Results from various simulations are presented and their implications discussed. Received: 26 June 1995 / Accepted in revised form: 30 June 1998     

Adaptive behavior with protozoa-inspired dynamics

A protozoa-inspired system for controlling autonomous robots is explained. The proposed system uses the nonlinear dynamics of the molecule concentrations in the cytoplasm of a protozoan. The model includes many parameters which are optimized using the genetic algorithm. A mobile robot obstacle avoidance example is shown with simulation results. The proposed protozoa-inspired system opens interesting possibilities to create new species by combining individual models by symbiotic or colony relationships. Received: 13 March 1996 / Accepted in revised form: 17 July 1998     

Predicting diversity of juvenile neotropical fish communities: patch dynamics versus habitat state in floodplain creeks

The species richness of communities should largely depend on habitat variability and/or on habitat state. We evaluated the ability of habitat variability and habitat state to predict the diversity of juvenile neotropical fish communities in creeks of a river floodplain. The young-fish fauna consisted of 73 taxa, and samples were well distributed over a wide range of relevant temporal and spatial habitat variability. We were unable to demonstrate clear patterns of richness in relation to temporal and spatial habitat variability (if habitat state variables were not included), regardless of the temporal variability scale, the grouping of sites (up- and downstream sites differed in temporal variability patterns), taxonomic units or life stages considered. Using stepwise multiple regression, 36% of the variance in species richness was explained for all data, and at best 47% was explained for all taxonomic units at upstream sites using temporal and spatial habitat variability and habitat state (bank length, mean width, mean water level before fishing and/or water turbidity). Using Monte Carlo simulations, we blindly predicted 31% (all data) and at best 37% (all upstream taxa) of the observed variance in species richness from these model types. This limited precision is probably because rare species produced most of the richness patterns in our creeks. The prediction of these rare species is generally difficult for various reasons, and may be a problem in many ecosystem types. Received: 6 July 1998 / Accepted: 16 November 1998     

Spectroscopic investigation of nickel cation binding with adenine mononucleotides: stability and structure of the 1:2 complex with adenosine 5′-monophosphate

 The interaction of Ni(II) ions with adenine mononucleotides (5′-AMP, 3′-AMP, 2′-AMP, 2′,3′-cAMP, 3′,5′-cAMP) was studied in aqueous solution using Raman spectroscopy and ¹³C and ³¹P NMR paramagnetic relaxation measurements. Macrochelate structures were observed to form for all non-cyclic AMPs, with increasing stability in the series: 3′-AMP < 2′-AMP < 5′-AMP. N7 of adenine was found to be the key site of the Ni(II)-adenine interaction for all non-cyclic AMPs. For 2′-AMP, an alternative binding to the pyrimidine ring may also exist. The dependence of Raman spectra on AMP and Ni(II) concentration confirmed the existence of a stable 1 : 2 Ni(II)-(5′-AMP) complex, besides the 1 : 1 complexes. In this complex, the adenine moieties of both 5′-AMP molecules are situated close to Ni(II), and their relative orientations with respect to the cation are very similar. The paramagnetic relaxation enhancements of the carbons indicate that the nickel ion is not located in the plane of the adenine units, but that the line connecting Ni(II) and N7 deviates strongly from the adenine planes. Phosphates are outer-sphere coordinated by the cation. Findings from both methods have led us to propose possible global architectures of the complex. Received: 26 June 1998 / Accepted: 22 July 1998     

Nonlinear time-course of lumbar muscle fatigue using recurrence quantifications

 Isometric skeletal muscle fatigue is usually assumed to be a linear process based upon the monotonic decrease in spectral frequency of the EMG. Since spectral analysis by fast Fourier transform (FFT) constitutes a linear transformation of the data, the present study was designed to reevaluate the time-course of muscle fatigue with a nonlinear tool, recurrence quantification analysis (RQA). Surface EMG recordings were obtained from the multifidus muscle of 17 human subjects during isometric posture-holding of the upper torso. The process of muscle fatigue was found to be linear for 59% of the subjects by FFT criteria, but nonlinear for 76% by RQA criteria. As a demonstrative control, both slow and fast transients occurring within a nonlinear mathematical process could be accurately depicted by RQA, but not by FFT. It is concluded that assessment of EMG patterns by nonlinear techniques can give insight into the time-course of fatiguing muscles attributed to the summation of several nonlinear and competing processes. Received: 12 November 1998 / Accepted in revised form: 29 November 1999     

How do bees learn and recognize visual patterns?

The basic task of perceptual systems is the recognition and localization of objects. The central nervous system has to solve these problems on the basis of the excitation patterns of sensory nerves, in spite of the fact that these provide only ambiguous information about objects. Two processing principles seem to be fundamental for an efficient formation of object representations: the extraction of characteristic features and the ability to assess similarities between different objects. This article reviews investigations in which different training paradigms were applied in order to explore the honeybee's capacities to learn and recognize visual patterns. One aim of these experiments is to assess whether insects use similar processing mechanisms as vertebrates, for instance human beings. By comparing the computational performance of perceptual systems in animals with different evolutionary history we can hope to learn more about the operation of basic rules in nervous systems. “The messages which the brain receives have not the least similarity with the stimuli. They consist in pulses of given intensities and frequencies, characteristic for the transmitting nerve-fiber, which ends at a definite place of the cortex. ... From this information it produces the image of the world by a process which can metaphorically be called a consummate piece of combinatorial mathematics: it sorts out of the maze of indifferent and varying signals, invariant shapes and relations which form the world of ordinary experience.” Max Born (1949) Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Determination of the precision of spike timing in the visual cortex of anaesthetised cats

 Neuronal cortical spike trains contain precisely replicating patterns whose presence cannot be accounted for by chance production. A comparison of the number of triplets of spikes present two times with the number of doublets replicated three times in the same window duration gives a frequency-insensitive measure of this type of fine temporal organisation. By varying the tolerance with which such precisely replicating patterns are detected, one can evaluate the accuracy of spike timing in spike trains. In the sample of data here analysed, it was found that replicating patterns were best seen in the precision range 0.4–1.4 ms (a result evidently at variance with a simple ‘integrate and fire’ model of neurons). Surprisingly, the fine temporal structure of spike trains thus evidenced was stronger at relatively low firing rate discharges and was present in both the ‘spontaneous’ and ‘evoked’ responses. Received: 3 April 1995/Accepted in revised form: 11 July 1995     

Minimal growth conservation of potato microplants: silver thiosulfate reduces ethylene-induced growth abnormalities during prolonged storage in vitro

 Efficacy of silver thiosulfate (STS) in reducing ethylene-induced culture abnormalities during minimal growth conservation of microplants was studied in seven potato (Solanum tuberosum L.) genotypes. Different concentrations of STS (0, 1.5, 3.0, 4.5, 6.0, 7.5 and 9.0 μg ml^–1) were tested in minimal growth medium based on MS medium supplemented with 20 g l^–1 mannitol and 40 g l^–1 sucrose. STS improved the microplant growth and reduced the culture abnormalities during prolonged maintenance of potato shoot cultures in vitro. The beneficial effect of STS was most prominent for number of green leaves per microplant and leaf senescence. After 16 months of storage, desirable microplant growth was observed in cultures conserved in medium containing 6.0–9.0 μg ml^–1 STS. The profile of the peroxidase isozymes of conserved cultures did not show any apparent genetic variation due to the presence of STS in the conservation medium. Received: 2 September 1998 / Revision received: 20 November 1998 / Accepted: 12 December 1998     

Iterative manual control model of human operator

In this paper, we present an iterative manual control model of a human operator performing some repetitive task. Various aspects of the model are discussed in detail. Experiments have been done to study the human capability to perform the tasks by learning iteratively. Results of the experiments show the ability of the human operator to perform the tracking of a desired trajectory for some unknown non-linear system with quite reasonable accuracy during the iteration process. It is concluded that the human operator performs the repetitive task by modifying his control action using error and error rate in each iteration. During the modification, the human operator assigns different weights to the error and error rate in each iteration. These results can be implemented in designing more efficient iterative learning control algorithms. Received: 29 September 1998 / Accepted in revised form: 12 May 1999     

Forming independent components via temporal locking of reconstruction architectures: a functional model of the hippocampus

The assumption is made that the formulation of relations as independent components (IC) is a main feature of computations accomplished by the brain. Further, it is assumed that memory traces made of non-orthonormal ICs make use of feedback architectures to form internal representations. Feedback then leads to delays, and delays in cortical processing form an obstacle to this relational processing. The problem of delay compensation is formulated as a speed-field tracking task and is solved by a novel control architecture. It is shown that in addition to delay compensation the control architecture can also shape long-term memories to hold independent components if a two-phase operation mode is assumed. Features such as a trisynaptic loop and a recurrent collateral structure at the second stage of that loop emerge in a natural fashion. Based on these properties a functional model of the hippocampal loop is constructed. Received: 18 March 1997 / Accepted in revised form: 30 June 1998     

Wide-field, motion-sensitive neurons and matched filters for optic flow fields

 The receptive field organization of a class of visual interneurons in the fly brain (vertical system, or VS neurons) shows a striking similarity to certain self-motion-induced optic flow fields. The present study compares the measured motion sensitivities of the VS neurons (Krapp et al. 1998) to a matched filter model for optic flow fields generated by rotation or translation. The model minimizes the variance of the filter output caused by noise and distance variability between different scenes. To that end, prior knowledge about distance and self-motion statistics is incorporated in the form of a “world model”. We show that a special case of the matched filter model is able to predict the local motion sensitivities observed in some VS neurons. This suggests that their receptive field organization enables the VS neurons to maintain a consistent output when the same type of self-motion occurs in different situations. Received: 14 June 1999 / Accepted in revised form: 20 March 2000     

Interpretation of nitrogen isotope signatures using the NIFTE model

Nitrogen cycling in forest soils has been intensively studied for many years because nitrogen is often the limiting nutrient for forest growth. Complex interactions between soil, microbes, and plants and the consequent inability to correlate δ¹⁵N changes with biologic processes have limited the use of natural abundances of nitrogen isotopes to study nitrogen (N) dynamics. During an investigation of N dynamics along the 250-year-old successional sequence in Glacier Bay, Alaska, United States, we observed several puzzling isotopic patterns, including a consistent decline in δ¹⁵N of the late successional dominant Picea at older sites, a lack of agreement between mineral N δ¹⁵N and foliar δ¹⁵N, and high isotopic signatures for mycorrhizal fungi. In order to understand the mechanisms creating these patterns, we developed a model of N dynamics and N isotopes (Nitrogen Isotope Fluxes in Terrestrial Ecosystems, NIFTE), which simulated the major transformations of the N cycle and predicted isotopic signatures of different plant species and soil pools. Comparisons with field data from five sites along the successional sequence indicated that NIFTE can duplicate observed patterns in δ¹⁵N of soil, foliage, and mineral N over time. Different scenarios that could account for the observed isotopic patterns were tested in model simulations. Possible mechanisms included increased isotopic fractionation on mineralization, fractionation during the transfer of nitrogen from mycorrhizal fungi to plants, variable fractionation on uptake by mycorrhizal fungi compared to plants, no fractionation on mycorrhizal transfer, and elimination of mycorrhizal fungi as a pool in the model. The model results suggest that fractionation during mineralization must be small (˜2‰), and that no fractionation occurs during plant or mycorrhizal uptake. A net fractionation during mycorrhizal transfer of nitrogen to vegetation provided the best fit to isotopic data on mineral N, plants, soils, and mycorrhizal fungi. The model and field results indicate that the importance of mycorrhizal fungi to N uptake is probably less under conditions of high N availability. Use of this model should encourage a more rigorous assessment of isotopic signatures in ecosystem studies and provide insights into the biologic transformations which affect those signatures. This should lead to an enhanced understanding of some of the fundamental controls on nitrogen dynamics. Received: 1 July 1998 / Accepted: 23 December 1998     

A model of activity-dependent formation of cerebellar microzones

According to modern views of the cerebellum in motor control, each cerebellar functional unit, or microzone, learns how to execute predictive and coordinative control, based on long-term depression of the granule cell-Purkinje cell synapses. In the present paper, in light of recent experimental and theoretical studies on synaptic elimination and cerebellar motor learning, a model of the formation of cerebellar microzones by climbing fiber synaptic elimination is proposed. It is shown that competition for an activity-dependent supply of neurotrophic factor can reproduce the spatio-temporal characteristics of climbing fiber synaptic elimination. It is further shown that when this elimination is accurate, motor coordination can be acquired in an arm reaching task. In view of the results of the present study, several predictions are proposed. Received: 19 January 1998 / Accepted in revised form: 22 April 1998     

Dynamics extraction in multivariate biomedical time series

A nonlinear analysis of the underlying dynamics of a biomedical time series is proposed by means of a multi-dimensional testing of nonlinear Markovian hypotheses in the observed time series. The observed dynamics of the original N-dimensional biomedical time series is tested against a hierarchy of null hypotheses corresponding to N-dimensional nonlinear Markov processes of increasing order, whose conditional probability densities are estimated using neural networks. For each of the N time series, a measure based on higher order cumulants quantifies the independence between the past of the N-dimensional time series, and its value r steps ahead. This cumulant-based measure is used as a discriminating statistic for testing the null hypotheses. Experiments performed on artificial and real world examples, including autoregressive models, noisy chaos, and nonchaotic nonlinear processes, show the effectiveness of the proposed approach in modeling multivariate systems, predicting multidimensional time series, and characterizing the structure of biological systems. Electroencephalogram (EEG) time series and heart rate variability trends are tested as biomedical signal examples. Received: 2 July 1997 / Accepted in revised form: 26 March 1998     

A holistic model for an internal representation to control the movement of a manipulator with redundant degrees of freedom

The paper proposes a model for the control of a multisegmented manipulator with redundant degrees of freedom. On the basis of an earlier model, the so-called MMC net, a simplified version is proposed here which has several advantages. First, it can easily be scaled up for the 3D case. Second, for the linear version a complete convergence proof is possible. Third, an easy way of implementing a damping parameter is shown. Fourth, the properties of the earlier model are unchanged, namely versatile control of the redundant system, immediate change from direct kinematics to inverse kinematics or any mixed control task, as well as robustness in the case of singularities. Received: 4 October 1997 / Accepted in revised form: 26 August 1998