What makes a neural microcircuit computationally powerful? Or more precisely, which measurable quantities could explain why one microcircuit C is better suited for a particular family of computational tasks than another microcircuit C'? One potential answer comes from results on cellular automata and random Boolean networks, where some evidence was provided that their computational power for offline computations is largest at the edge of chaos, i.e. at the transition boundary between order and chaos. We analyse in this article the significance of the edge of chaos for real time computations in neural microcircuit models consisting of spiking neurons and dynamic synapses. We find that the edge of chaos predicts quite well those values of circuit parameters that yield maximal computational power. But obviously it makes no prediction of their computational power for other parameter values. Therefore, we propose a new method for predicting the computational power of neural microcircuit models. The new measure estimates directly the kernel property and the generalization capability of a neural microcircuit. We validate the proposed measure by comparing its prediction with direct evaluations of the computational performance of various neural microcircuit models. This procedure is applied first to microcircuit models that differ with regard to the spatial range of synaptic connections and their strength, and then to microcircuit models that differ with regard to the level of background input currents, the conductance, and the level of noise on the membrane potential of neurons. In the latter case the proposed method allows us to quantify differences in the computational power and generalization capability of neural circuits in different dynamic regimes (UP- and DOWN-states) that have been demonstrated through intracellular recordings in vivo.

Developmental robotics is an emerging field located at the intersection of robotics, cognitive science and developmental sciences. This paper elucidates the main reasons and key motivations behind the convergence of fields with seemingly disparate interests, and shows why developmental robotics might prove to be beneficial for all fields involved. The methodology advocated is synthetic and two-pronged: on the one hand, it employs robots to instantiate models originating from developmental sciences; on the other hand, it aims to develop better robotic systems by exploiting insights gained from studies on ontogenetic development. This paper gives a survey of the relevant research issues and points to some future research directions.

Keywords: developmental robotics, artificial intelligence

Summary: A mobile robot should be designed to navigate with collision avoidance capability in the real world, flexibly coping with the changing environment. In this paper, a novel limit-cycle navigation method is proposed for a fast mobile robot using the limit-cycle characteristics of a 2nd-order nonlinear function. It can be applied to the robot operating in a dynamically changing environment, such as in a robot soccer system. By adjusting the radius of the motion circle and the direction of obstacle avoidance, the navigation method proposed enables a robot to maneuver smoothly towards any desired destination. Simulations and real experiments using a robot soccer system demonstrate the merits and practical applicability of the proposed method.

Keywords: robot soccer; navigation; limit cycle; real-time control

Invariant features of temporally varying signals are useful for analysis and classification. Slow feature analysis (SFA) is a new method for learning invariant or slowly varying features from a vectorial input signal. SFA is based on a non-linear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative. It is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features, which are ordered by their degree of invariance. SFA can be applied hierarchically to process high dimensional input signals and to extract complex features. Slow feature analysis is applied first to complex cell tuning properties based on simple cell output including disparity and motion. Then, more complicated input-output functions are learned by repeated application of SFA. Finally, a hierarchical network of SFA-modules is presented as a simple model of the visual system. The same unstructured network can learn translation, size, rotation, contrast, or, to a lesser degree, illumination invariance for one-dimensional objects, depending only on the training stimulus. Surprisingly, only a few training objects sufficed to achieve good generalization to new objects. The generated representation is suitable for object recognition. Performance degrades, if the network is trained to learn multiple invariances simultaneously.

Summary: A novel hierarchical neural network architecture for sensory-motor learning and behavior generation is proposed. Two levels of forward model neural networks are operated on different time scales while parametric interactions are allowed between the two network levels in the bottom-up and top-down directions. The models are examined through experiments of behavior learning and generation using a real robot arm equipped with a vision system. The results of the learning experiments showed that the behavioral patterns are learned by self-organizing the behavioral primitives in the lower level and combining the primitives sequentially in the higher level. The results contrast with prior work by Pawelzik et al. [Neural Comput. 8, 340 (1996)], Tani and Nolfi [From animals to animats, 1998], and Wolpert and Kawato [Neural Networks 11, 1317 (1998)] in that the primitives are represented in a distributed manner in the network in the present scheme whereas, in the prior work, the primitives were localized in specific modules in the network. Further experiments of on-line planning showed that the behavior could be generated robustly against a background of real world noise while the behavior plans could be modified flexibly in response to changes in the environment. It is concluded that the interaction between the bottom-up process of recalling the past and the top-down process of predicting the future enables both robust and flexible situated behavior.

Keywords: Learning; Behavior; Articulation; Chunking

The positive-feedback nature of Hebbian plasticity can destabilize the properties of neuronal networks. Recent work has demonstrated that this destabilizing influence is counteracted by a number of homeostatic plasticity mechanisms that stabilize neuronal activity. Such mechanisms include global changes in synaptic strengths, changes in neuronal excitability, and the regulation of synapse number. These recent studies suggest that Hebbian and homeostatic plasticity often target the same molecular substrates, and have opposing effects on synaptic or neuronal properties. These advances significantly broaden our framework for understanding the effects of activity on synaptic function and neuronal excitability.

Summary: We propose that the ability to extract regularities from time series through prediction learning can be enhanced if we use a hierarchical architecture in which higher layers are trained to predict the internal state of lower layers when such states change significantly. This hierarchical organization has two functions: (a) it forces the system to recode sensory information progressively so as to enhance useful regularities and filter out useless information; and (b) it progressively reduces the length of the sequences which should be predicted going from lower to higher layers. This, in turn, allows higher levels to extract higher-level regularities which are hidden at the sensory level. By training an architecture of this type to predict the next sensory state of a robot navigating in an environment divided in two rooms, we show how the first-level prediction layer extracts low-level regularities, while the second-level prediction layer extracts higher-level regularities.

Keywords: prediction learning; development; mobile robotics

During learning and development, neural circuitry is refined, in part, through changes in the number and strength of synapses. Most studies of long-term changes in synaptic strength have concentrated on Hebbian mechanisms, where these changes occur in a synapse-specific manner. While Hebbian mechanisms are important for modifying neuronal circuitry selectively, they might not be sufficient because they tend to destabilize the activity of neuronal networks. Recently, several forms of homeostatic plasticity that stabilize the properties of neural circuits have been identified. These include mechanisms that regulate neuronal excitability, stabilize total synaptic strength, and influence the rate and extent of synapse formation. These forms of homeostatic plasticity are likely to go 'hand-in-glove' with Hebbian mechanisms to allow experience to modify the properties of neuronal networks selectively.

We propose that a regulation mechanism based on Hebbian covariance plasticity may cause the brain to operate near criticality. We analyze the effect of such a regulation on the dynamics of a network with excitatory and inhibitory neurons and uniform connectivity within and across the two populations. We show that, under broad conditions, the system converges to a critical state lying at the common boundary of three regions in parameter space; these correspond to three modes of behavior: high activity, low activity, oscillation.

This paper provides an overview of the bottom-up approach to AI, commonly referred to as behavior-oriented AI. The behavior-oriented approach, with its focus on the interaction between autonomous agents and their environments, is introduced by contrasting it with the traditional approach of knowledge-based AI. Different notions of autonomy are discussed, and key problems of generating adaptive and complex behavior are identified. A number of techniques for the generation of behavior are introduced and evaluated regarding their potential for realizing different aspects of autonomy, as well as adaptivity and complexity of behavior. It is concluded that, in order to realize truly autonomous and intelligent agents, the behavior-oriented approach will have to focus even more on lifelike qualities in both agents and environments. (Author)

Keywords: Artifical life and evolutionary robotics

The automated construction of dynamic system models is an important application area for ILP. We describe a method that learns qualitative models from time-varying physiological signals. The goal is to understand the complexity of the learning task when faced with numerical data, what signal processing techniques are required, and how this affects learning. The qualitative representation is based on Kuipers' QSIM. The learning algorithm for model construction is based on Coiera's GENMODEL. We show that QSIM models are efficiently PAC learnable from positive examples only, and that GENMODEL is an ILP algorithm for efficiently constructing a QSIM model. We describe both GENMODEL which performs RLGG on qualitative states to learn a QSIM model, and the front-end processing and segmenting stages that transform a signal into a set of qualitative states. Next we describe results of experiments on data from six cardiac bypass patients. Useful models were obtained, representing both normal and abnormal physiological states. Model variation across time and across different levels of temporal abstraction and fault tolerance is explored. The assumption made by many previous workers that the abstraction of examples from data can be separated from the learning task is not supported by this study. Firstly, the effects of noise in the numerical data manifest themselves in the qualitative examples. Secondly, the models learned are directly dependent on the initial qualitative abstraction chosen.

Keywords: SIMULATION, inductive logic programming, qualitative modelling, system identification, PAC learning, physiological modelling, cardiovascular system, data mining, patient monitoring

Feasibility of applying evolutionary methods to automatically generating controllers for physical mobile robots. Overview state of the art, main approaches, key challenges, unanswered problems, promising directions

Keywords: genetic algorithms, genetic programming, robots

Feasibility of applying evolutionary methods to automatically generating controllers for physical mobile robots. Overview state of the art, main approaches, key challenges, unanswered problems, promising directions

Keywords: genetic algorithms, genetic programming, robots

Keywords: Data Mining, Classification, Decision-Trees, MDL

A new incremental network model for supervised learning is proposed. The model builds up a structure of units each of which has an associated local linear mapping (LLM). Error information obtained during training is used to determine where to insert new units whose LLMs are interpolated from their neighbors. Simulation results for several classification tasks indicate fast convergence as well as good generalization. The ability of the model to also perform function approximation is demonstrated by an example. 1 Introduction Local (or piece-wise) linear mappings (LLMs) are an economic means of describing a }wellbehaved { function f : R n ! R m . The principle is to approximate the function (which may be given by a number of input/output samples (; i) 2 R n Theta R m ) with a set of linear mappings each of which is constrained to a local region of the input space R n . LLM-based methods have been used earlier to learn the inverse kinematics of robot arms [7], for classificat...

Keywords: AI AGENT OVERVIEW VISION KNOWLEDGE-REP REACTIVE

The paper proposes a mechanism for the spontaneous formation of perceptually grounded meanings under the selectionist pressure of a discrimination task. The mechanism is defined formally and the results of some simulation experiments are reported.

Keywords: genetic algorithms, genetic programming

Additive unsupervised learning structure. Can be extended with RBFs to get supervised learning, RBFs are positioned automatically. Good results.

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's).Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture.We also develop an on-line learning algorithm in which the parameters are updated incrementally.Comparative simulation results are presented in the robot dynamics domain.

We describe a project to capitalize on newly available levels of computational resources in order to understand human cognition. We will build an integrated physical system including vision, sound input and output, and dextrous manipulation, all controlled by a continuously operating large scale parallel MIMD computer. The resulting system will learn to ``think'' by building on its bodily experiences to accomplish progressively more abstract tasks. Past experience suggests that in attempting to build such an integrated system we will have to fundamentally change the way artificial intelligence, cognitive science, linguistics, and philosophy think about the organization of intelligence. We expect to be able to better reconcile the theories that will be developed with current work in neuroscience.

The dynamics of nonlinear systems often vary qualitatively over their parameter space. Methodologies for designing piecewise control laws for dynamical systems, such as gain scheduling, are useful because they circumvent the problem of determining a single global model of the plant dynamics. Instead, the dynamics are approximated using local models that vary with the plant's operating point. When a controller is learned instead of designed, analogous issues arise. This article describes a multi-network, or modular, neural network architecture that learns to perform control tasks using a piecewise control strategy. The architecture's networks compete to learn the training patterns. As a result, a plant's parameter space is adaptively partitioned into a number of regions, and a different network learns a control law in each region. This learning process is described in a probabilistic framework and learning algorithms that perform gradient ascent in a log likelihood function are discussed. Simulations show that the modular architecture's performance is superior to that of a single network on a multipayload robot motion control task.

This is the first volume in the series WAVELET ANALYSIS AND ITS APPLICATIONS. It is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and and time-frequency analysis. Among the basic topics covered are time frequency localization, intergral wavelet transforms, dyadic wavelets, frames, spine wavelets, orthonormal wavelet bases, and wavelet packets. Is is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject.

Keywords: An Overview, Fourier Analysis, Wavelet Transforms and Time-frequency Analysis, Cardinal Spline Analysis, scaling functions and Wavelets, Cardinal Spline Wavelets, Orthogonal Wavelets and Wavelet Packets

Automatic classification of active sonar signals using the Wigner-Ville transform (WVT), the wavelet transform (WT) and the scalogram is addressed. Features are extracted by integrating over regions in the time-frequency (TF) distribution, and are classified by a decision tree. Experimental results show classification and detection rates of up to 92 WVT and the scalogram, particularly at high noise levels. This can be partially attributed to the absence of cross terms in the WT.

Book only: ISBN 1-55860-238-0 $ 44.95 U.S. $49.45 International Book and Software: ISBN 1-55860-240-2 $69.95 U.S. $76.00 International Software only: ISBN 1-55860-239-9 $34.95 U.S. $38.45 International 1 Introduction 2 Constructing Decision Trees 3 Unknown Attribute Values 4 Pruning Decision Trees 5 From Trees to Rules 6 Windowing 7 Grouping Attribute Values 8 Interacting with Classification Models 9 Guide to Using the System 10 Limitations 11 Desirable Additions

Keywords: book, decision trees, C4.5, ID3, inductive inference, II, rule rules

The Behavior Language is a rule-based real-time parallel robot programming language originally based on ideas from [Brooks 86], [Connell 89], and [Maes 89]. It compiles into a modified and extended version of the subsumption architecture [Brooks 86] and thus has backends for a number of processors including the Motorola 68000 and 68HC11, the Hitachi 6301, and Common Lisp. Behaviors are groups of rules which are activatable by a number of different schemes. There are no shared data structures across behaviors, but instead all communication is by explicit message passing. All rules are assumed to run in parallel and asynchronously. It includes the earlier notions of inhibition and suppression, along with a number of mechanisms for spreading of activation.

Keywords: vector quantization | speech | competitive learning

We argue that generally accepted methodologies of artificial intelligence research are limited in the proportion of human level intelligence they can be expected to emulate. We argue that the currently accepted decompositions and static representations used in such research are wrong. We argue for a shift to a process based model, with a decomposition based on task achieving behaviors as the organizational principle. In particular we advocate building robotic insects.

[For the entire collection see Zbl. 741.68016.]

The authors' effort to build a situated knowledge-based system resultet in a cooperative hybrid system called DDT ( device diagnostic tool). DDT is a hybrid symbolic/connectionist system, embodying cooperativity and self-tuning capabilities, thus being able to face the problem of model explosion cycle. The approach is illustrated using a real-life expert system in the domain of technical troubleshooting.

Keywords: situated knowledge-based system; device diagnostic tool

The articles of this volume will be reviewed individually.

Keywords: Hoegaarden (Belgium); Workshop; Proceedings; EKAW '94; Knowledge acquisition

The paper proposes a set of principles and a general architecture that may explain how language and meaning may originate and complexify in a group of physically grounded distributed agents. An experimental setup is introduced for concretising and validating specific mechanisms based on these principles. The setup consists of two robotic heads that watch static or dynamic scenes and engage in language games, in which one robot describes to the other what they see. The first results from experiments showing the emergence of distinctions, of a lexicon, and of primitive syntactic structures are reported.

Keywords: symbolic models; robotic agents; origins of language and meaning

Summary: A mobile robot should be designed to navigate with collision avoidance capability in the real world, flexibly coping with the changing environment. In this paper, a novel limit-cycle navigation method is proposed for a fast mobile robot using the limit-cycle characteristics of a 2nd-order nonlinear function. It can be applied to the robot operating in a dynamically changing environment, such as in a robot soccer system. By adjusting the radius of the motion circle and the direction of obstacle avoidance, the navigation method proposed enables a robot to maneuver smoothly towards any desired destination. Simulations and real experiments using a robot soccer system demonstrate the merits and practical applicability of the proposed method.

Keywords: robot soccer; navigation; limit cycle; real-time control

Summary: The paper surveys some of the mechanisms that have been demonstrated to be relevant for evolving communication systems in software simulations or robotic experiments. In each case, precursors or parallels with work in the study of artificial life and adaptive behaviour are discussed.

Summary: The problem of category learning has been traditionally investigated by employing disembodied categorization models. One of the basic tenets of embodied cognitive science states that categorization can be interpreted as a process of sensory-motor coordination, in which an embodied agent, while interacting with its environment, can structure its own input space for the purpose of learning about categories. Many researchers, including John Dewey and Jean Piaget, have argued that sensory-motor coordination is crucial for perception and for development. In this paper we give a quantitative account of why sensory-motor coordination is important for perception and category learning.

Summary: The paper describes a system for open-ended communication by autonomous robots about event descriptions anchored in reality through the robot's sensori-motor apparatus. The events are dynamic and agents must continually track changing situations at multiple levels of detail through their vision system. We are specifically concerned with the question how grounding can become shared through the use of external (symbolic) representations, such as natural language expressions.

Keywords: Autonomous Robots; Event Descriptions; Open-Ended

Summary: A novel hierarchical neural network architecture for sensory-motor learning and behavior generation is proposed. Two levels of forward model neural networks are operated on different time scales while parametric interactions are allowed between the two network levels in the bottom-up and top-down directions. The models are examined through experiments of behavior learning and generation using a real robot arm equipped with a vision system. The results of the learning experiments showed that the behavioral patterns are learned by self-organizing the behavioral primitives in the lower level and combining the primitives sequentially in the higher level. The results contrast with prior work by Pawelzik et al. [Neural Comput. 8, 340 (1996)], Tani and Nolfi [From animals to animats, 1998], and Wolpert and Kawato [Neural Networks 11, 1317 (1998)] in that the primitives are represented in a distributed manner in the network in the present scheme whereas, in the prior work, the primitives were localized in specific modules in the network. Further experiments of on-line planning showed that the behavior could be generated robustly against a background of real world noise while the behavior plans could be modified flexibly in response to changes in the environment. It is concluded that the interaction between the bottom-up process of recalling the past and the top-down process of predicting the future enables both robust and flexible situated behavior.

Keywords: Learning; Behavior; Articulation; Chunking

Entire collection CS 2004.019000G

A behavior system consists of the components and control programs necessary to establish a particular behavior in a robotic agent. The paper proposes a mathematical approach for the analysis of behavior systems. The approach rests on viewing a behavior system as a dynamical system whose equilibrium state is attained when the behavior it is responsible for is achieved.

Keywords: behavior system; robotic agent; dynamical system; equilibrium state; autonomous agent

The paper describes how symbolic processes are self-organized in the navigational learning of a mobile robot. Based on a dynamical system's approach, the paper shows that the forward modeling scheme based on recurrent neural network (RNN) learning is capable of extracting grammatical structure hidden in the geometry of the workspace from navigational experience. This robot is capable of mentally simulating its own actions using the acquired forward model. The paper shows that such a mental process by the RNN can naturally be situated with respect to the behavioural contexts, provided that the forward model learned is embedded on the global attractor. The internal representation obtained is proved to be grounded, since it is self-organized solely through itnteraction with the physical world. The paper shows also that structural stability arises in the interaction between the neural dynamics and the environment dynamics, accounting for the situatedness of the internal symbolic process.

Keywords: self-organization of symbolic processes; robot navigation; situatedness of symbolic processes

The paper discusses a novel scheme for sensory-based navigation of a mobile robot. In our previous work (Tani & Fukumura, 1994, Neural Networks, 7(3), 553-563), we formulated the problem of goal-directed navigation as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded in an adequate sensory-based internal state space so that a unique mapping from the internal state space to the motor command could be established. In the current formulation a recurrent neural network is employed, which shows that an adequate internal state space can be self-organized, through supervised training with sensorimotor sequences. The experiment was conducted using a real mobile robot equipped with a laser range sensor, demonstrating the validity of the presented scheme by working in a noisy real-world environment.

Keywords: neural networks; sensory motor system; mobile robot; navigation learning

This paper describes the use of the C4.5 decision tree learning algorithm in the design of a classifier for a new approach to the mapping of a mobile robot's local environment. The decision tree uses the features from the echoes of an ultrasonic array mounted on the robot to classify the contours of its local environment. The contours are classified into a finite number of two dimensional shapes to form a primitive map which is to be used for navigation. The nature of the problem, noise and the practical timing constraints, distinguishes it from those typically used in machine learning applications and highlights some of the advantages of decision tree learning in robotic applications.

Ideally, sensory information forms the only source of information to a robot. We consider an algorithm for the self-organization of a controller. At short time scales the controller is merely reactive but the parameter dynamics and the acquisition of knowledge by an internal model lead to seemingly purposeful behavior on longer time scales. As a paradigmatic example, we study the simulation of an underactuated snake-like robot. By interacting with the real physical system formed by the robotic hardware and the environment, the controller achieves a sensitive and body-specific actuation of the robot.

Homeokinetic learning provides a route to the self-organization of elementary behaviors in autonomous robots by establishing low-level sensomotoric loops. Strength and duration of the internal parameter changes which are caused by the homeokinetic adaptation provide a natural evaluation of external states, which can be used to incorporate information from additional sensory inputs and to extend the function of the low-level behavior to more general situations. We illustrate the approach by two examples, a mobile robot and a human-like hand which are driven by the same low-level scheme, but use the second-order information in different ways to achieve either risk avoidance and unconstrained movement or constrained movement. While the low-level adaptation follows a set of rigid learning rules, the second-order learning exerts a modulatory effect to the elementary behaviors and to the distribution of their inputs.

The paper presents a method to guide the self-organised development of behaviours of autonomous robots. In earlier publications we demonstrated how to use the homeokinesis principle and dynamical systems theory to obtain self-organised playful but goal-free behaviour. Now we extend this framework by reinforcement signals. We validate the mechanisms with two experiment with a spherical robot. The first experiment aims at fast motion, where the robot reaches on average about twice the speed of a not reinforcement robot. In the second experiment spinning motion is rewarded and we demonstrate that the robot successfully develops pirouettes and curved motion which only rarely occur among the natural behaviours of the robot.

Self-organization and the phenomenen of emergence play an essential role in living systems and form a challenge to artificial life systems. This is not only because systems become more life like but also since self-organization may help in reducing the design efforts in creating complex behavior systems. The present paper exemplifies a general approach to the self-organization of behavior which has been developed and tested in various examples in recent years. We apply this approach to a spherical robot driven by shifting internal masses. The complex physics of this robotic object is completely unknown to the controller. Nevertheless after a short time the robot develops systematic rolling movements covering large distances with high velocity. In a hilly landscape it is capable of manoeuvering out of the basins and in landscapes with a fixed rotational geometry the robot more or less adatps its movements to this geometry - the controller so to say develops a kind of feeling for its environment although there are no sensors for measuring the positions or the velocity of the robot. We argue that this behavior is a result of the spontaneous symmetry breaking effects which are responsible for the emergence of behavior in our approach.

Self-organization and the phenomenon of emergence play an essential role in living systems and form a challenge to artificial life systems. This is not only because systems become more lifelike, but also since self-organization may help in reducing the design efforts in creating complex behavior systems. The present paper studies self-exploration based on a general approach to the self-organization of behavior, which has been developed and tested in various examples in recent years. This is a step towards autonomous early robot development. We consider agents under the close sensorimotor coupling paradigm with a certain cognitive ability realized by an internal forward model. Starting from tabula rasa initial conditions we overcome the bootstrapping problem and show emerging self-exploration. Apart from that, we analyze the effect of limited actions, which lead to deprivation of the world model. We show that our paradigm explicitly avoids this by producing purposive actions in a natural way. Examples are given using a simulated simple wheeled robot and a spherical robot driven by shifting internal masses.

Keywords: autonomous robots, self-organization, homeostasis, homeokinesis, dynamical systems, learning

Despite the tremendous progress in robotic hardware and in both sensorial and computing efficiencies the performance of contemporary autonomous robots is still far below that of simple animals. This has triggered an intensive search for alternative approaches to the control of robots. The present paper exemplifies a general approach to the self-organization of behavior which has been developed and tested in various examples in recent years. We apply this approach to an underactuated snake like artifact with a complex physical behavior which is not known to the controller. Due to the weak forces available, the controller so to say has to develop a kind of feeling for the body which is seen to emerge from our approach in a natural way with meandering and rotational collective modes being observed in computer simulation experiments.