The Analysis of Mammalian Hearing Systems Supports the Hypothesis That Criticality Favors Neuronal Information Representation but Not Computation.

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.

Excess Entropies Suggest the Physiology of Neurons to Be Primed for Higher-Level Computation.

Biological neuronal networks excel over artificial ones in many ways, but the origin of this is still unknown. Our symbolic dynamics-based tool of excess entropies suggests that neuronal cultures naturally implement data structures of a higher level than what we expect from artificial neural networks, or from close-to-biology neural networks. This points to a new pathway for improving artificial neural networks towards a level demonstrated by biology.

Second-order phase transition in phytoplankton trait dynamics.

Key traits of unicellular species, such as cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here, we reveal new empirical scaling evidence associated with a transition in the population and the chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This "criticality hypothesis" can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology.

Universality in the firing of minicolumnar-type neural networks.

An open question in biological neural networks is whether changes in firing modalities are mainly an individual network property or whether networks follow a joint pathway. For the early developmental period, our study focusing on a simple network class of excitatory and inhibitory neurons suggests the following answer: Networks with considerable variation of topology and dynamical parameters follow a universal firing paradigm that evolves as the overall connectivity strength and firing level increase, as seen in the process of network maturation. A simple macroscopic model reproduces the main features of the paradigm as a result of the competition between the fundamental dynamical system notions of synchronization vs chaos and explains why in simulations the paradigm is robust regarding differences in network topology and largely independent from the neuron model used. The presented findings reflect the first dozen days of dissociated neuronal in vitro cultures (upon following the developmental period bears similarly universal features but is characterized by the processes of neuronal facilitation and depression that do not require to be considered for the first developmental period).

Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks.

There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality. This suggests that the different fingerprints may pertain to distinct phenomena.

Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State.

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response.

Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale invariance, from a general level, applicable to all dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., neuronal Hodgkin-Huxley equations). When subject to natural "signal coupling," ensembles of Hopf systems below the bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs at parameter values substantially below where the average of the individual systems would bifurcate, with a frequency profile that is sharpened if compared to the individual systems.

Universal dynamical properties preclude standard clustering in a large class of biochemical data.

MOTIVATION: Clustering of chemical and biochemical data based on observed features is a central cognitive step in the analysis of chemical substances, in particular in combinatorial chemistry, or of complex biochemical reaction networks. Often, for reasons unknown to the researcher, this step produces disappointing results. Once the sources of the problem are known, improved clustering methods might revitalize the statistical approach of compound and reaction search and analysis. Here, we present a generic mechanism that may be at the origin of many clustering difficulties. RESULTS: The variety of dynamical behaviors that can be exhibited by complex biochemical reactions on variation of the system parameters are fundamental system fingerprints. In parameter space, shrimp-like or swallow-tail structures separate parameter sets that lead to stable periodic dynamical behavior from those leading to irregular behavior. We work out the genericity of this phenomenon and demonstrate novel examples for their occurrence in realistic models of biophysics. Although we elucidate the phenomenon by considering the emergence of periodicity in dependence on system parameters in a low-dimensional parameter space, the conclusions from our simple setting are shown to continue to be valid for features in a higher-dimensional feature space, as long as the feature-generating mechanism is not too extreme and the dimension of this space is not too high compared with the amount of available data. AVAILABILITY AND IMPLEMENTATION: For online versions of super-paramagnetic clustering see http://stoop.ini.uzh.ch/research/clustering. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Beyond scale-free small-world networks: cortical columns for quick brains.

We study to what extent cortical columns with their particular wiring boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic--intercolumnar--scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks.

A full computation-relevant topological dynamics classification of elementary cellular automata.

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos."

Why Hearing Aids Fail and How to Solve This.

Hearing is one of the human's foremost sensors; being able to hear again after suffering from a hearing loss is a great achievement, under all circumstances. However, in the long run, users of present-day hearing aids and cochlear implants are generally only halfway satisfied with what the commercial side offers. We demonstrate here that this is due to the failure of a full integration of these devices into the human physiological circuitry. Important parts of the hearing network that remain unestablished are the efferent connections to the cochlea, which strongly affects the faculty of listening. The latter provides the base for coping with the so-called cocktail party problem, or for a full enjoyment of multi-instrumental musical plays. While nature clearly points at how this could be remedied, to achieve this technologically will require the use of advanced high-precision electrodes and high-precision surgery, as we outline here. Corresponding efforts must be pushed forward by coordinated efforts from the side of science, as the commercial players in the field of hearing aids cannot be expected to have a substantial interest in advancements into this direction.

Exploiting deterministic features in apparently stochastic data.

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.

Financial markets' deterministic aspects modeled by a low-dimensional equation.

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.

Principles and typical computational limitations of sparse speaker separation based on deterministic speech features.

The separation of mixed auditory signals into their sources is an eminent neuroscience and engineering challenge. We reveal the principles underlying a deterministic, neural network-like solution to this problem. This approach is orthogonal to ICA/PCA that views the signal constituents as independent realizations of random processes. We demonstrate exemplarily that in the absence of salient frequency modulations, the decomposition of speech signals into local cosine packets allows for a sparse, noise-robust speaker separation. As the main result, we present analytical limitations inherent in the approach, where we propose strategies of how to deal with this situation. Our results offer new perspectives toward efficient noise cleaning and auditory signal separation and provide a new perspective of how the brain might achieve these tasks.

Analysis of the "Sonar Hopf" cochlea.

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.

Note on the Reliability of Biological vs. Artificial Neural Networks.

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.

Local cochlear correlations of perceived pitch.

Pitch is one of the most salient attributes of the human perception of sound, but is still not well understood. This difficulty originates in the entwined nature of the phenomenon, in which a physical stimulus as well as a psychophysiological signal receiver are involved. In an electronic realization of a biophysically detailed nonlinear model of the cochlea, we find local cochlear correlates of the perceived pitch that explain all essential pitch-shifting phenomena from physical grounds.

Real-world existence and origins of the spiral organization of shrimp-shaped domains.

In two-dimensional parameter spaces, nonlinear systems producing solutions of a fixed periodicity form islands of a characteristic shape, called "shrimp"-shaped domains (SSDs). In simulations of electronic circuits, SSDs of different periodicities were recently found to be connected along spirals. By means of a hardware realization of the simulations, we provide a first direct proof of the real-world existence of this phenomenon. An improved description establishes a close experiment-simulation correspondence, and a simplified circuit family demonstrates the homoclinic saddle-focus origin of the phenomenon.

Hebbian self-organizing integrate-and-fire networks for data clustering.

We propose a Hebbian learning-based data clustering algorithm using spiking neurons. The algorithm is capable of distinguishing between clusters and noisy background data and finds an arbitrary number of clusters of arbitrary shape. These properties render the approach particularly useful for visual scene segmentation into arbitrarily shaped homogeneous regions. We present several application examples, and in order to highlight the advantages and the weaknesses of our method, we systematically compare the results with those from standard methods such as the k-means and Ward's linkage clustering. The analysis demonstrates that not only the clustering ability of the proposed algorithm is more powerful than those of the two concurrent methods, the time complexity of the method is also more modest than that of its generally used strongest competitor.

Periodic orbit analysis demonstrates genetic constraints, variability, and switching in Drosophila courtship behavior.

We use symbolic dynamics to describe Drosophila courtship communication. We posit that behavior should be defined in terms of irreducible periodic orbits of fundamental acts. This leads to a first operational definition of behavior, which allows for a fine grained quantitative analysis of behavior. We obtain evidence that during Drosophila courtship, individual characteristics of the protagonists are exchanged (predominantly from the male to the female) and that males in the presence of fruitless males perform a behavioral switch from male to female behavior.