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Abstract Many processes in nature are the result of many coupled individual subsystems (like population dynamics or neurosystems). Not always such systems exhibit simple stable behaviors that in the past science has mostly focused on. Often, these systems are characterized by bursts of seemingly stochastic activity, interrupted by quieter periods. The hypothesis is that the presence of a strong deterministic ingredient is often obscured by the stochastic features. We test this by modeling classically stochastic considered real-world data from both, the stochastic as well as the deterministic approaches to find that the deterministic approach’s results level with those from the stochastic side. Moreover, the deterministic approach is shown to reveal the full dynamical systems landscape, which can be exploited for steering the dynamics into a desired regime.

Abstract We ask whether empirical finance market data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity), with their recently observed alternations between calm periods and financial turmoil, could be described by a low-dimensional deterministic model, or whether this requests a stochastic approach. We find that a deterministic model performs at least as well as one of the best stochastic models, but may offer additional insight into the essential mechanisms that drive financial markets.

Various types of neural networks are currently widely used in diverse technical applications, not least because neural networks are known to be able to “generalize.” The latter property raises expectations that they should be able to handle unexpected situations with similar success than humans. Using fundamental examples, we show that in situations for which they have not been trained, artificial approaches tend to run into substantial problems, which highlights a deficit in comparisons to human abilities. For this problem–which seems to have obtained little attention so far–we provide a first analysis, based on simple examples, which exhibits some key features responsible for the difference between human and artificial intelligence.

In the neighborhood of critical states, distinct materials exhibit the same physical behavior, expressed by common simple laws among measurable observables, hence rendering a more detailed analysis of the individual systems obsolete. It is a widespread view that critical states are fundamental to neuroscience and directly favor computation. We argue here that from an evolutionary point of view, critical points seem indeed to be a natural phenomenon. Using mammalian hearing as our example, we show, however, explicitly that criticality does not describe the proper computational process and thus is only indirectly related to the computation in neural systems.

The “Sonar Hopf” cochlea is a recently much advertised engineering design of an auditory sensor. We analyze this approach based on a recent description by its inventors Hamilton, Tapson, Rapson, Jin, and van Schaik, in which they exhibit the “Sonar Hopf” model, its analysis and the corresponding hardware in detail. We identify problems in the theoretical formulation of the model and critically examine the claimed coherence between the described model, the measurements from the implemented hardware, and biological data.

An important step towards understanding the working principles of the mammalian hearing sensor is the concept of an active cochlear amplifier. Theoretical arguments and physiological measurements suggest that the active cochlear amplifiers originate from systems close to a Hopf bifurcation. Efforts to model the mammalian hearing sensor on these grounds have, however, either had problems in reproducing sufficiently close essential aspects of the biological example (Magnasco, M.O. Phys. Rev. Lett. 90, 058101 (2003); Duke, T. & Jülicher, F. Phys. Rev. Lett. 90, 158101 (2003)), or required complicated spatially coupled differential equation systems that are unfeasible for transient signals (Kern, A. & Stoop, R. Phys. Rev. Lett. 91, 128101 (2003)). Here, we demonstrate a simple system of electronically coupled Hopf amplifiers that not only leads to the desired biological response behavior, but also has real-time capacity. The obtained electronic Hopf cochlea shares all salient signal processing features exhibited by the mammalian cochlea and thus provides a simple and efficient design of an artificial mammalian hearing sensor.

Using a symbolic dynamics and a surrogate data approach, we show that the language exhibited by common fruit flies Drosophila ('D.') during courtship is as grammatically complex as the most complex human-spoken modern languages. This finding emerges from the study of fifty high-speed courtship videos (generally of several minutes duration) that were visually frame-by-frame dissected into 37 fundamental behavioral elements. From the symbolic dynamics of these elements, the courtship-generating language was determined with extreme confidence (significance level > 0.95). The languages categorization in terms of position in Chomsky's hierarchical language classification allows to compare Drosophila's body language not only with computer's compiler languages, but also with human-spoken languages. Drosophila's body language emerges to be at least as powerful as the languages spoken by humans.

Staircase-like structures in the log-log correlation plot of a time series indicate patterns against a noisy background, even under condition of strong jitter. We analyze the method for different jitter-noise-combinations, using quantitative criteria to measure the achievement by the method. A phase diagram shows the remarkable potential of this method even under very unfavorable conditions of noise and jitter. Moreover, we provide a novel and compact analytical derivation of the upper and lower bounds on the number of steps observable in the ideal noiseless case, as a function of pattern length and embedding dimension. The quantitative measure developed combined with the ideal bounds can serve as guiding lines for determining potential periodicity in noisy data.

Activity pattern modalities of neuronal ensembles are determined by node properties as well as network structure. For many purposes, it is of interest to be able to relate activity patterns to either node properties or to network properties (or to a combination of both). When in physiological neural networks we observe bursting on a coarse-grained time and space scale, a proper decision on whether bursts are the consequence of individual neurons with an inherent bursting property or whether we are dealing with a genuine network effect has generally not been possible because of the noise in these systems. Here, by linking different orders of time and space scales, we provide a simple coarse-grained criterion for deciding this question.