[Show abstract][Hide abstract] ABSTRACT: Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.
[Show abstract][Hide abstract] ABSTRACT: Tsunamis exhibit surprisingly strong height fluctuations. An in-depth understanding of the mechanisms that lead to these variations in wave height is a prerequisite for reliable tsunami forecasting. It is known, for example, that the presence of large underwater islands or the shape of the tsunami source can affect the wave heights. Here we show that the consecutive effect of even tiny fluctuations in the profile of the ocean floor (the bathymetry) can cause unexpectedly strong fluctuations in the wave height of tsunamis, with maxima several times higher than the average wave height. A novel approach combining stochastic caustic theory and shallow water wave dynamics allows us to determine the typical propagation distance at which the strongly focused waves appear. We demonstrate that owing to this mechanism the small errors present in bathymetry measurements can lead to drastic variations in predicted tsunami heights. Our results show that a precise knowledge of the ocean’s bathymetry is absolutely indispensable for reliable tsunami forecasts.
[Show abstract][Hide abstract] ABSTRACT: Spontaneous bursting activity in cultured neuronal networks is initiated by leader neurons, which constitute a small subset of first-to-fire neurons forming a sub-network that recruits follower neurons into the burst. While the existence and stability of leader neurons is well established, the influence of stimulation on the leader-follower dynamics is not sufficiently understood. By combining multi-electrode array recordings with whole field optical stimulation of cultured Channelrhodopsin-2 transduced hippocampal neurons, we show that fade-in photo-stimulation induces a significant shortening of intra-burst firing rate peak delay of follower electrodes after offset of the stimulation compared to unperturbed spontaneous activity. Our study shows that optogenetic stimulation can be used to change the dynamical fine structure of self-organized network bursts.
[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.
Full-text · Article · Jun 2014 · Frontiers in Systems Neuroscience
[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.
Preview · Article · Jun 2014 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: The search for models of self-organized criticality in neural networks started before the first experiments demonstrated examples of the critical brain. One of the early models, the Eurich model, predicted critical exponents and various dynamical regimes that were experimentally observed, but failed to describe a mechanism for the self-organization of criticality.In contrast to simultaneous attempts, the LHG model did not only describe a route to criticality in neural systems but also turned out to be simple enough for analytical treatment. Interestingly, it showed also greater biological plausibility than the Eurich model. When the synapses in the network obey a realistic dynamics, the critical region in the parameter space increases and becomes infinite in the large system limit. This effect of depressive synapses can be interpreted as a feedback control mechanism that drives the system toward the critical state.If also facilitation is included in the synaptic dynamics the critical region extends even more. In the latter case an analytical treatment is still possible and reveals an interesting type of stationary state consisting of self-organized critical phase and a subcritical phase that has not been described earlier. The phases are connected by first- and second-order phase transitions which form a cusp bifurcation. Switching between phases can be induced by synchronized activity or by activity deprivation.Having the model established, we ask how the network topology, synaptic homeostasis, neural leakage, and long-term learning affect the critical behavior of the network. We demonstrate that all main topology types (random, small-world, scale-free) permit critical avalanches. We conclude with a discussion of astonishing fact that various types of adaptivity in neural systems appear to cooperate in order to enable robust critical behavior.
[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.
Full-text · Article · Nov 2013 · Physical Review Letters
[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.
Full-text · Article · Oct 2013 · Frontiers in Neural Circuits
[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: 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.
[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.
[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.
Preview · Article · Jun 2013 · New Journal of Physics
[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: 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: Random caustics are a ubiquitous phenomenon of ray or particle propagation through weakly disordered media. They lead to a pronounced branching not only of the ray or particle flow density but also in the intensity of corresponding wave flows. In this talk I will present our results on the stochastic theory of random caustics, showing that the number of caustics generated by a random medium follows a universal law, and will discuss the impact of branching on the intensity statistics of wave flows.