Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.Comment: 17 pages, 5 figure

Emergent complex neural dynamics

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain

Gravitational collapse with tachyon field and barotropic fluid

A particular class of space-time, with a tachyon field, \phi, and a barotropic fluid constituting the matter content, is considered herein as a model for gravitational collapse. For simplicity, the tachyon potential is assumed to be of inverse square form i.e., V(\phi) \sim \phi^{-2}. Our purpose, by making use of the specific kinematical features of the tachyon, which are rather different from a standard scalar field, is to establish the several types of asymptotic behavior that our matter content induces. Employing a dynamical system analysis, complemented by a thorough numerical study, we find classical solutions corresponding to a naked singularity or a black hole formation. In particular, there is a subset where the fluid and tachyon participate in an interesting tracking behaviour, depending sensitively on the initial conditions for the energy densities of the tachyon field and barotropic fluid. Two other classes of solutions are present, corresponding respectively, to either a tachyon or a barotropic fluid regime. Which of these emerges as dominant, will depend on the choice of the barotropic parameter, \gamma. Furthermore, these collapsing scenarios both have as final state the formation of a black hole.Comment: 18 pages, 7 figures. v3: minor changes. Final version to appear in GR

Pedestrian, Crowd, and Evacuation Dynamics

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of crowds in panic or evacuation situations, methods to optimize building designs for egress, and factors potentially causing the breakdown of orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c

Aspects of astrocyte energy metabolism, amino acid neurotransmitter homoeostasis and metabolic compartmentation

Astrocytes are key players in brain function; they are intimately involved in neuronal signalling processes and their metabolism is tightly coupled to that of neurons. In the present review, we will be concerned with a discussion of aspects of astrocyte metabolism, including energy-generating pathways and amino acid homoeostasis. A discussion of the impact that uptake of neurotransmitter glutamate may have on these pathways is included along with a section on metabolic compartmentation

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

Modeling complex ecological economic systems: toward an evolutionary, dynamic understanding of people and nature

Recent understanding about system dynamics and predictability that has emerged from the study of complex systems is creating new tools for modeling interactions between anthropogenic and natural systems. A range of techniques has become available through advances in computer speed and accessibility and by implementing a broad, interdisciplinary systems view

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma=1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task. Results Neither the LFP nor the subsampled SOC models showed a power law for f(s). Both, f(s) and sigma, depended sensitively on the subsampling geometry and the dynamics of the model. Only one of the SOC models, the Abelian Sandpile Model, exhibited f(s) and sigma similar to those calculated from LFP activity. Conclusions Since subsampling can prevent the observation of the characteristic power law and sigma in SOC systems, misclassifications of critical systems as sub- or supercritical are possible. Nevertheless, the system specific scaling of f(s) and sigma under subsampling conditions may prove useful to select physiologically motivated models of brain function. Models that better reproduce f(s) and sigma calculated from the physiological recordings may be selected over alternatives

Quasi-Neutral theory of epidemic outbreaks

Some epidemics have been empirically observed to exhibit outbreaks of all possible sizes, i.e., to be scalefree or scale-invariant. Different explanations for this finding have been put forward; among them there is a model for "accidental pathogens" which leads to power-law distributed outbreaks without apparent need of parameter fine tuning. This model has been claimed to be related to self-organized criticality, and its critical properties have been conjectured to be related to directed percolation. Instead, we show that this is a (quasi) neutral model, analogous to those used in Population Genetics and Ecology, with the same critical behavior as the voter-model, i.e. the theory of accidental pathogens is a (quasi)-neutral theory. This analogy allows us to explain all the system phenomenology, including generic scale invariance and the associated scaling exponents, in a parsimonious and simple way.Comment: 13 pages, 6 figures Accepted for publication in PLoS ONE the text have been modified in orden to improve the figure's resolutio

Valence isomerization of 2-phospha-4-silabicyclo[1.1.0]butane: a high-level ab initio study

The rearrangements for 2-phospha-4-silabicyclo[1.1.0]butane, analogous to the valence isomerization of the hydrocarbons bicyclobutane, 1,3-butadiene, and cyclobutene, were studied at the (U)QCISD(T)/6-311+G**//(U)QCISD/6-31G* level of theory. The monocyclic 1,2-dihydro-1,2-phosphasiletes are shown to be the thermodynamically preferred product, in contrast to the isomerization of the hydrocarbons, which favors the 1,3-butadiene structure. Furthermore, an unprecedented direct isomerization pathway to the 1,2-dihydro-1,2-phosphasiletes was identified. This pathway is competitive with the isomerization via the open-chain butadienes and becomes favorable when electron-donating substituents are present on silicon