[Show abstract][Hide abstract] ABSTRACT: The magnitude and variability of Earth’s biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework are in agreement with paleontologic databases.
[Show abstract][Hide abstract] ABSTRACT: In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.
[Show abstract][Hide abstract] ABSTRACT: Waves traveling through random media exhibit random focusing that leads to
extremely high wave intensities even in the absence of nonlinearities. Although
such extreme events are present in a wide variety of physical systems and the
statistics of the highest waves is important for their analysis and forecast,
it remains poorly understood in particular in the regime where the waves are
highest. We suggest a new approach that greatly simplifies the mathematical
analysis and calculate the scaling and the distribution of the highest waves
valid for a wide range of parameters.
[Show abstract][Hide abstract] ABSTRACT: Neuronal dynamics are fundamentally constrained by the underlying structural
network architecture, yet much of the details of this synaptic connectivity are
still unknown even in neuronal cultures in vitro. Here we extend a previous
approach based on information theory, the Generalized Transfer Entropy, to the
reconstruction of connectivity of simulated neuronal networks of both
excitatory and inhibitory neurons. We show that, due to the model-free nature
of the developed measure, both kinds of connections can be reliably inferred if
the average firing rate between synchronous burst events exceeds a small
minimum frequency. Furthermore, we suggest, based on systematic simulations,
that even too weak spontaneous inter-burst rates could be raised to meet the
requirements of our reconstruction algorithm by applying a weak spatially
homogeneous stimulation to the entire network. By combining multiple recordings
of the same in silico network before and after pharmacologically blocking
inhibitory synaptic transmission, we show then how it is possible to infer with
high confidence the excitatory or inhibitory nature of each individual neuron.
[Show abstract][Hide abstract] ABSTRACT: Waves traveling through weakly random media are known to be strongly affected by their corresponding ray dynamics, in particular in forming linear freak waves. The ray intensity distribution, which, e.g., quantifies the probability of freak waves is unknown, however, and a theory of how it is approached in an appropriate semiclassical limit of wave mechanics is lacking. We show that this limit is not the usual limit of small wavelengths, but that of decoherence. Our theory, which can describe the intensity distribution for an arbitrary degree of coherence is relevant to a wide range of physical systems, as decoherence is omnipresent in real systems.
[Show abstract][Hide abstract] ABSTRACT: We investigate the geometric properties of two-dimensional continuous time random walks that are used extensively to model stochastic processes exhibiting anomalous diffusion in a variety of different fields. Using the concept of subordination, we determine exact analytical expressions for the average perimeter and area of the convex hulls for this class of non-Markovian processes. As the convex hull is a simple measure to estimate the home range of animals, our results give analytical estimates for the home range of foraging animals that perform sub-diffusive search strategies such as some Mediterranean seabirds and animals that ambush their prey. We also apply our results to Levy flights where possible.
New Journal of Physics 06/2013; 15(6):063034. · 4.06 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Central neurons operate in a regime of constantly fluctuating conductances,
induced by thousands of presynaptic cells. Channelrhodopsins have been almost
exclusively used to imprint a fixed spike pattern by sequences of brief
depolarizations. Here we introduce continuous dynamic photostimulation
(CoDyPs), a novel approach to mimic in-vivo like input fluctuations
noninvasively in cells transfected with the weakly inactivating
channelrhodopsin variant ChIEF. Even during long-term experiments, cultured
neurons subjected to CoDyPs generate seemingly random, but reproducible spike
patterns. In voltage clamped cells CoDyPs induced highly reproducible current
waveforms that could be precisely predicted from the light-conductance transfer
function of ChIEF. CoDyPs can replace the conventional, flash-evoked imprinting
of spike patterns in in-vivo and in-vitro studies, preserving natural activity.
When combined with non-invasive spike-detection, CoDyPs allows the acquisition
of order of magnitudes larger data sets than previously possible, for studies
of dynamical response properties of many individual neurons.
[Show abstract][Hide abstract] ABSTRACT: This article discusses the compositional structure of hand movements by analyzing and modeling neural and behavioral data obtained from experiments where a monkey (Macaca fascicularis) performed scribbling movements induced by a search task. Using geometrically based approaches to movement segmentation, it is shown that the hand trajectories are composed of elementary segments that are primarily parabolic in shape. The segments could be categorized into a small number of classes on the basis of decreasing intra-class variance over the course of training. A separate classification of the neural data employing a hidden Markov model showed a coincidence of the neural states with the behavioral categories. An additional analysis of both types of data by a data mining method provided evidence that the neural activity patterns underlying the behavioral primitives were formed by sets of specific and precise spike patterns. A geometric description of the movement trajectories, together with precise neural timing data indicates a compositional variant of a realistic synfire chain model. This model reproduces the typical shapes and temporal properties of the trajectories; hence the structure and composition of the primitives may reflect meaningful behavior.
Frontiers in Computational Neuroscience 01/2013; 7:103. · 2.48 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Critical behavior in neural networks is characterized by scale-free avalanche size distributions and can be explained by self-regulatory mechanisms. Theoretical and experimental evidence indicates that information storage capacity reaches its maximum in the critical regime. We study the effect of structural connectivity formed by Hebbian learning on the criticality of network dynamics. The network only endowed with Hebbian learning does not allow for simultaneous information storage and criticality. However, the critical regime can be stabilized by short-term synaptic dynamics in the form of synaptic depression and facilitation or, alternatively, by homeostatic adaptation of the synaptic weights. We show that a heterogeneous distribution of maximal synaptic strengths does not preclude criticality if the Hebbian learning is alternated with periods of critical dynamics recovery. We discuss the relevance of these findings for the flexibility of memory in aging and with respect to the recent theory of synaptic plasticity.
Frontiers in Computational Neuroscience 01/2013; 7:87. · 2.48 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Neurons in the brain are wired into a synaptic network that spans
multiple scales, from local circuits within cortical columns to fiber
tracts interconnecting distant areas. However, brain function require
the dynamic control of inter-circuit interactions on time-scales faster
than synaptic changes. In particular, strength and direction of causal
influences between neural populations (described by the so-called
directed functional connectivity) must be reconfigurable even when the
underlying structural connectivity is fixed. Such directed functional
influences can be quantified resorting to causal analysis of time-series
based on tools like Granger Causality or Transfer Entropy. The ability
to quickly reorganize inter-areal interactions is a chief requirement
for performance in a changing natural environment. But how can manifold
functional networks stem "on demand" from an essentially fixed
structure? We explore the hypothesis that the self-organization of
neuronal synchronous activity underlies the control of brain functional
connectivity. Based on simulated and real recordings of critical
neuronal cultures in vitro, as well as on mean-field and spiking network
models of interacting brain areas, we have found that "function follows
dynamics", rather than structure. Different dynamic states of a same
structural network, characterized by different synchronization
properties, are indeed associated to different functional digraphs
(functional multiplicity). We also highlight the crucial role of
dynamics in establishing a structure-to-function link, by showing that
whenever different structural topologies lead to similar dynamical
states, than the associated functional connectivities are also very
similar (structural degeneracy).
[Show abstract][Hide abstract] ABSTRACT: Synchronized bursting is found in many brain areas and has also been implicated in the pathophysiology of neuropsychiatric disorders such as epilepsy, Parkinson's disease, and schizophrenia. Despite extensive studies of network burst synchronization, it is insufficiently understood how this type of network wide synchronization can be strengthened, reduced, or even abolished. We combined electrical recording using multi-electrode array with optical stimulation of cultured channelrhodopsin-2 transducted hippocampal neurons to study and manipulate network burst synchronization. We found low frequency photo-stimulation protocols that are sufficient to induce potentiation of network bursting, modifying bursting dynamics, and increasing interneuronal synchronization. Surprisingly, slowly fading-in light stimulation, which substantially delayed and reduced light-driven spiking, was at least as effective in reorganizing network dynamics as much stronger pulsed light stimulation. Our study shows that mild stimulation protocols that do not enforce particular activity patterns onto the network can be highly effective inducers of network-level plasticity.
Frontiers in Neural Circuits 01/2013; 7:167. · 3.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Random caustics and branching are ubiquitous phenomena of ray and wave propagation through weakly disordered media. I will present results on the stochastic theory of branching, and its impact on intensity statistics of wave flows.
[Show abstract][Hide abstract] ABSTRACT: The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Lévy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems.
Physical Review E 10/2012; 86(4-1):041134. · 2.31 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances [1,2]. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.  HH et al., PLoS ONE,6,e26457 (2011).  Physics Today, invited article, submitted (2012).
The Journal of the Acoustical Society of America 09/2012; 132(3):2042. · 1.65 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [Reichenbach, Mobilia, and Frey, Nature (London) 448, 1046 (2007)], we find that the emergence of spirals results in an ambiguous behavior regarding the stability of coexistence. The typical time until extinction exhibits, however, a qualitatively opposite dependence on the newly introduced nonunit carrying capacity in the spiraling and the nonspiraling regimes. This allows us to determine a critical mobility that marks the onset of this spiraling state sharply. In contrast, we demonstrate that the conventional finite size stability analysis with respect to spatial size is of limited use for identifying the onset of the spiraling regime.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 08/2012; 86(2).
[Show abstract][Hide abstract] ABSTRACT: A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.
[Show abstract][Hide abstract] ABSTRACT: We demonstrate that branching of the electron flow in semiconductor
nanostructures can strongly affect macroscopic transport quantities and can
significantly change their dependence on external parameters compared to the
ideal ballistic case even when the system size is much smaller than the mean
free path. In a corner-shaped ballistic device based on a GaAs/AlGaAs
two-dimensional electron gas we observe a splitting of the commensurability
peaks in the magnetoresistance curve. We show that a model which includes a
random disorder potential of the two-dimensional electron gas can account for
the random splitting of the peaks that result from the collimation of the
electron beam. The shape of the splitting depends on the particular realization
of the disorder potential. At the same time magnetic focusing peaks are largely
unaffected by the disorder potential.
[Show abstract][Hide abstract] ABSTRACT: Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question "Which areas cause the present activity of which others?". Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this "communication-through-coherence", making thus possible a fast "on-demand" reconfiguration of global information routing modalities.
[Show abstract][Hide abstract] ABSTRACT: Branched flow is a universal phenomenon of particle and wave flows which
are subjected to weak, correlated disorder. It has been observed on
length scales ranging from a few micrometres, affecting the transport
properties of semiconductor devices , up to several thousand
kilometres, influencing sound propagation through the ocean . It is
also responsible for the appearance of large and hazardous freak waves
and tsunamis . While the statistics of the number of such branches
has recently been calculated , the influence on the statistics of the
intensity of the waves remains an open question . Here, we show how
the classical ray intensity impacts on the wave intensity statistics,
and illuminate the role played by the decoherence of the
wavefunction. Topinka et al., Nature 410, 183 (2001), Jura et al.,
Nat. Phys. 3, 841 (2007) Wolfson & Tomsovich, J. Acous. Soc. Am.
109, 2693 (2001) Berry, Proc. R. Soc. A 463, 3055 (2007); Heller et
al., J. Geophys. Res. 113, C09023 (2008) Metzger, Fleischmann and
Geisel, Phys. Rev. Lett. 105, 020601 (2010) H"ohmann et al., Phys.
Rev. Lett. 104, 093901 (2010), Arecchi et al., Phys. Rev. Lett. 106,
153901 (2011), Ying et al., Nonlinearity 24, R67 (2011)
[Show abstract][Hide abstract] ABSTRACT: It is a long standing question why in the mammalian eye photoreceptors
are positioned at the back of the retina, forcing photons to travel
through various neuronal layers of the retina before the light-sensitive
rods and cones can detect them. Recent studies suggest that certain
retinal glial cells--called M"uller cells (MCs)--play an important role
in answering that question. It has been experimentally shown that MCs
extracted from the retina can act as optical fibers . To understand
the light guiding properties of the MC in the natural fluctuating
optical environment, we developed a model to analyze the light
reflection and transmission of MCs embedded in a random medium neuronal
tissue. With these quantities and a simplified geometrical eye model we
study how light is scattered in the eye. We found that MCs can lead to a
substantial increase of the signal-to-noise ratio (SNR), the ratio of
the intensity of direct incident light at a photoreceptor to the
intensity of back-scattered light from other areas of the retina. The
SNR is most pronounced in the vicinity of the fovea and can be more than
an order of magnitude.[4pt]  Franze et. al., Proc Natl Acad Sci USA,
2007, 104, 8287-8292.