For concreteness, we propose and discuss a framework which mimics emotions on a functional level. Based on time allocation via emotional stationarity (TAES), emotions are implemented as abstract criteria, such as satisfaction, challenge and boredom, which serve to evaluate activities that have been carried out. The resulting timeline of experienced emotions is compared with the `character' of the agent, which is defined in terms of a preferred distribution of emotional states. The long-term goal of the agent, to align experience with character, is achieved by optimizing the frequency for selecting individual tasks. Upon optimization, the statistics of emotion experience becomes stationary.

Model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.

The effectiveness of the presented mechanisms was tested numerically using different external input protocols. The network performance after adaptation was evaluated by training the network to perform a time delayed XOR operation on binary sequences. As our main result, we found that flow control can reliably regulate the spectral radius under different input statistics, but precise tuning is negatively affected by interneural correlations. Furthermore, flow control showed a consistent task performance over a wide range of input strengths/variances. Variance control, on the other side, did not yield the desired spectral radii with the same precision. Moreover, task performance was less consistent across different input strengths.

Given the better performance and simpler mathematical form of flow control, we concluded that a local control of the spectral radius via an implicit adaptation scheme is a realistic alternative to approaches using classical “set point” homeostatic feedback controls of neural firing.

The symmetry of bipartite lattices allows states in which all active sites are located alternatingly on one of the two sublattices, A and B, respectively for even and odd times. We show that the AB-sublattice symmetry is spontaneously broken for the AAS model, an observation that holds also for the Manna model. One finds that a metastable AB-symmetry conserving state is transiently observable and that it has the potential to influence the width of the scaling regime, in particular in two dimensions.

The AAS model mimics the behavior of integrate-and-fire neurons which propagate activity independently of the input received, as long as the threshold is crossed. Abstracting from regular lattices, one can identify sites with neurons and consider quenched networks of neurons connected to a fixed number G of other neurons, with G being drawn from a suitable distribution. The neuronal activity is then propagated to G other neurons. The AAS model is hence well suited for theoretical studies of nearly critical brain dynamics. We also point out that the waiting-time distribution allows an avalanche-free experimental access to criticality.

The distribution of album lifetimes evolved during the last decades from a log-normal distribution to a powerlaw, a profound change. Presenting an information-theoretical approach to human activities, we suggest that the fading relevance of personal time horizons may be causing this phenomenon. Furthermore we find that sales and airplay based charts differ statistically and that the inclusion of streaming affects chart diversity adversely.

We point out in addition that opinion dynamics may accelerate not only in cultural domains, as found here, but also in other settings, in particular in politics, where it could have far reaching consequences.

We study the emergence of autonomous task switching for the case of a simulated robot arm. Grasping one of several moving objects corresponds in this setting to a specific activity. Overall, the arm should follow a given object temporarily and then move away, in order to search for a new target and reengage. We show that this behavior can be generated robustly when modeling the arm as an adaptive dynamical system. The dissipation function is in this approach time dependent. The arm is in a dissipative state when searching for a nearby object, dissipating energy on approach. Once close, the dissipation function starts to increase, with the eventual sign change implying that the arm will take up energy and wander off. The resulting explorative state ends when the dissipation function becomes again negative and the arm selects a new target. We believe that our approach may be generalized to generate self-organized sequences of activities in general.

Our robot interacts with the environment by monitoring the state of its actuators, that is via propriosensation. External sensors are absent. In a structured environment the robot shows complex emergent behavior that includes pushing movable blocks around, reversing direction when hitting a wall and turning when climbing a slope. On flat grounds the robot wiggles in a snake-like manner, when moving at higher velocities. We also investigate the emergence of motor primitives, viz the route to locomotion, which is characterized by a series of local and global bifurcations in terms of dynamical system theory.

Genesis missions raise important ethical issues, in particular with regard to planetary protection. Here we argue that exoplanetary and planetary protection differ qualitatively as a result of the vastly different cruising times for payload delivering probes, which are of the order of millennia for interstellar probes, but only of years for solar system bodies. Furthermore we point out that our galaxy may harbor a large number of habitable exoplanets, M-dwarf planets, which could be sterile due to the presence of massive primordial oxygen atmospheres. We believe that the prospect terrestrial life has in our galaxy would shift on a fundamental level in case that the existence of this type of habitable but sterile oxygen planets will be corroborated by future research. It may also explain why our sun is not a M dwarf, the most common star type, but a medium-sized G-class star.

We study different implementations of kick control for the case of simulated and real-world wheeled robots, for which the dynamics of the distinct wheels is generated independently by local feedback loops. The feedback loops are mediated by rate-encoding neurons disposing exclusively of propriosensoric inputs in terms of projections of the actual rotational angle of the wheel. The changes of the neural activity are then transmitted into a rotational motion by a simulated transmission rod akin to the transmission rods used for steam locomotives.

We find that the self-organized attractor landscape may be morphed both by higher-level control signals, in the spirit of kick control, and by interacting with the environment. Bumping against a wall destroys the limit cycle corresponding to forward motion, with the consequence that the dynamical variables are then attracted in phase space by the limit cycle corresponding to backward moving. The robot, which does not dispose of any distance or contact sensors, hence reverses direction autonomously.

We consider here systems, in which the overall dynamics settles in the limit of long times either in a limit cycle switching between transient states, or in a chaotic attractor. The set of target points then decomposes into one-dimensional (or fractal) branches, which can be analyzed directly. Here we examine the role of target points as transiently stable attractors in an autonomously active recurrent neural network. We quantify their influence on the transient states by measuring the effective distance between trajectories and the corresponding target points in phase space. We also present an example of chaotic dynamics, discussing how the chaotic motion is related to the set of transient attractors.

The network considered contains, for certain parameters settings, symmetry protected solutions in the form of travelling waves. We find, that the slow manifold does not guide the flow in this regime, which we denote as non-adiabatic, even though there are up to four orders of magnitude difference between the slow and the fast time scales.

For the case of a sample high speed transit to Proxima Centauri we find that magnetic momentum braking would involve daunting mass requirements of the order of 10³ tons. A low speed mission to the Trappist-1 system could be realized on the other side already with a 1.5 ton spacecraft, which would be furthermore compatible with the specifications of currently envisioned directed energy launch systems. The extended cruising times of the order of 10⁴ years imply however that a mission to the Trappist-1 system would be viable only for mission concepts for which time constrains are not relevant.

We review here our current understanding of the processes determining the timescales shaping the geo-evolution of an earth-like planet, the prospect of finding Genesis candidate planets and selected issues regarding the mission layout. Discussing the ethical aspects connected with a Genesis mission, which would be expressively not for human benefit, we will also touch the risk that a biosphere incompatibility may arise in the wake of an eventual manned exploration of a second earth.

We find that a wide palette of motion patterns are generated through the interaction of STSP, robot, and environment (closed-loop configuration), including various forward meandering and circular motions, together with chaotic trajectories. The observed locomotion is robust with respect to additional interactions with obstacles. In the chaotic phase the robot is seemingly engaged in actively exploring its environment. We believe that our results constitute a concept of proof that transient synaptic plasticity, as described by STSP, may potentially be important for the generation of motor commands and for the emergence of complex locomotion patterns, adapting seamlessly also to unexpected environmental feedback.

Induced (by collisions) and spontaneous mode switching are observed. We find that locomotion may follow transiently unstable limit cycles. The degeneracy of the propagating state with respect to the direction of propagating is, in our analysis, one of the drivings for the chaotic wandering, which partly involves a smooth diffusion of the angle of propagation.

On the theory side there has been, lively activity in developing new and extended models. Three classes of models have emerged. The first line of models is based on a separation between the time scales of drive and dissipation, and includes the original sandpile model and its extensions, like the dissipative earthquake model. Within this approach the steady state is close to criticality in terms of an absorbing phase transition. The second line of approach is based on external drives and internal dynamics competing on similar time scales and includes the coherent noise model, which has a non-critical steady state characterized by heavy-tailed distributions. The third line of modeling proposes a non-critical state which is self-organizing, being guided by an optimization principle, such as the concept of highly optimized tolerance.

We present a comparative overview regarding distinct modeling approaches together with a discussion of their potential relevance as underlying generative models for real-world phenomena. The complexity of physical and biological scaling phenomena has been found to transcend the explanatory power of individual paradigmal concepts, like the theory of self-organized criticality, the interaction between theoretical development and experimental observations has been very fruitful, leading to a series of novel concepts and insights.

We include in our study the correlations between the in-degree and the Alexa traffic rank, a popular index for the traffic volume, finding non-trivial power-law correlations. We find that sites with more/less than about one Thousand links from different domains have remarkably different statistical properties, for all correlation functions studied, indicating towards an underlying hierarchical structure of the World Wide Web.

We investigate the influence of stress, in terms of conflicting optimization targets, on the resulting dynamics. Objective function stress is absent when the target level for the mean of neural activities is identical for the two generating functionals and the resulting latching dynamics is then found to be regular. Objective function stress is present when the respective target activity levels differ, inducing intermittent bursting latching dynamics.

We recapitulate the notion of criticality, as originally introduced in statistical physics for second order phase transitions, turning then to the discussion of critical dynamical systems. We elucidate in detail the difference between a 'critical system', viz a system on the verge of a phase transition, and a 'critical state', viz state with scale-invariant correlations, stressing the fact that the notion of universality is linked to critical states.

We then discuss rigorous results for two classes of critical dynamical systems, the Kauffman net and a vertex routing model, which both have non-critical states. However, an external observer that samples randomly the phase space of these two critical models, would find scale invariance. We denote this phenomenon as 'observational criticality' and discuss its relevance for the response properties of critical dynamical systems.

When observing experimentally a real-world dynamical system one normally samples stochastically its phase space. The number and the length of the attractors are then weighted by the size of their respective basins of attraction. This situation is equivalent to `on the fly' generation of routing tables for which we find power law scaling for the weighted average length of attractors, for both conserved routing models. These results show that critical dynamical systems are generically not scale-invariant, but may show power-law scaling when sampled stochastically. It is hence important to distinguish between intrinsic properties of a critical dynamical system and its behavior that one would observe when randomly probing its phase space.

It is however plausible that biological comparators emerge from self-organizing, genetically encoded principles, which allow the system to adapt to the changes in the input and in the organism. We propose an unsupervised neural circuitry, where the function of input comparison emerges via self-organization only from the interaction of the system with the respective inputs, without external influence or supervision.

The proposed neural comparator adapts, unsupervised, according to the correlations present in the input streams. The system consists of a multilayer feed-forward neural network which follows a local output minimization (anti-Hebbian) rule for adaptation of the synaptic weights. The local output minimization allows the circuit to autonomously acquire the capability of comparing the neural activities received from different neural populations, which may differ in the size of the population and in the neural encoding used. The comparator is able to compare objects never encountered before in the sensory input streams and to evaluate a measure of their similarity, even when differently encoded.

We examine here the question: Why do humans dispose of the diffusive emotional control system? Is this a coincidence, a caprice of nature, perhaps a leftover of our genetic heritage, or a necessary aspect of any advanced intelligence, being it biological or synthetic? We argue here that emotional control is necessary to solve the motivational problem, viz the selection of short-term utility functions, in the context of an environment where information, computing power and time constitute scarce resources.

We review our current understanding of the functional role of emotions, stressing the role of the neuromodulators mediating emotions for the diffusive homeostatic control system of the brain. We discuss a recent proposal, that emotional diffusive control is characterized, in contrast to neutral diffusive control, by interaction effects, viz by interferences between emotional arousal and reward signaling. Several proposals for the realization of synthetic emotions are discussed in this context, together with key open issues regarding the interplay between emotional motivational drives and diffusive control.

There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up?

We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, viz the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively.

For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

This review will start with a brief overview of the experimental efforts, together with a discussion of transient vs. self-sustained neural activity in the framework of reservoir computing. The main emphasis will be then on two paradigmal neural network architectures showing continuously ongoing transient-state dynamics: saddle point networks and networks of attractor relics.

Self-active neural networks are confronted with two seemingly contrasting demands: a stable internal dynamical state and sensitivity to incoming stimuli. We show, that this dilemma can be solved by networks of attractor relics based on competitive neural dynamics, where the attractor relics compete on one side with each other for transient dominance, and on the other side with the dynamical influence of the input signals. Unsupervised and local Hebbian-style online learning then allows the system to build up correlations between the internal dynamical transient states and the sensory input stream. An emergent cognitive capability results from this set-up. The system performs online, and on its own, a non-linear independent component analysis of the sensory data stream, all the time being continuously and autonomously active. This process maps the independent components of the sensory input onto the attractor relics, which acquire in this way a semantic meaning.

• Graph Theory and Small-World Networks;
• Chaos, bifurcations and diffusion;
• Complexity and Information Theory;
• Random Boolean Networks;
• Cellular Automata and Self-Organized Criticality;
• Darwinian Evolution, Hypercyles and Game Theory;
• Synchronization Phenomena;
• Elements of Cognitive System Theory.

We present numerical estimates for Delta_R/Delta_S from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. An analysis of the numerical Raman intensity leads us to postulate a continuum of two-magnon bound states in the Spin-Peierls phase. We discuss in detail the numerical method used, the dependence of the results on the model parameters and a novel matrix-element effect due to the dimerization of the Raman-operator in the Spin-Peierls phase.