List of poster contributions

Ansmann, Gerrit	Generating mechanisms of Extreme Events in Oscillator Networks	Abstract
Bajic, Djordje	Instability of genetic networks to internal perturbations	Abstract
Bhattacharya, Joydeep	Signature of Genre Specific Musical Creativity on Cortical Network Patterns: A Pilot Study	Abstract
Bialonski, Stephan	Data-driven prediction of extreme events in high-dimensional excitable systems	Abstract
Bianco-Martinez, Ezequiel	Information based approach for data analysis and network inference	Abstract
Casadiego Bastidas, Jose Luis	Network Dynamics as an Inverse Problem: Reconstruction from Time Series	Abstract
Dana, Syamal	Amplitude death and lag synchronization in coupled oscillators: a common mechanism	Abstract
Dana, Syamal	Amplitude death and oscillation death in coupled dynamical system: Mechanisms of transition	Abstract
Di Bernardi Luft, Caroline	The effect of graded and categorical feedback on learning related global synchronization	Abstract
Dickten, Henning	Measuring delay directed interactions with symbolic transfer entropy	Abstract
Dods, Joe	A dynamic network analysis of space weather activity as observed in multiple ground based magnetometer stations	Abstract
Elsegai, Heba	Network Inference in the Presence of Latent Confounders	Abstract
Gascoyne, Daniel	Non-Linear Dynamics of Learning and its Application to Colour Identification	Abstract
Geier, Christian	Is the epileptic focus the most important region in epileptic brain networks?	Abstract
Hallerberg, Sarah	Predicting and triggering long jumps and sticks in molecular diffusion	Abstract
Hens, Chittaranjan	Chimera state in globally coupled chaotic oscillators.	Abstract
Hens, Chittaranjan	Extreme Multistability in network of oscillators.	Abstract
Hernandez Lahme, Damian Gabriel	High-order interactions between words in written language	Abstract
Hlinka, Jaroslav	Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information	Abstract
Jajcay, Nikola	Granger causality estimate of information flow in temperature fields is consistent with wind direction	Abstract
Ji, Peng	Cluster Explosive Synchronization in Complex Networks	Abstract
Kishore, Vimal	Extreme events and network failures	Abstract
Korbel, Jan	Rényi transfer entropy and its application for intraday financial data	Abstract
Liang, X. San	Information flow/transfer: a rigorous formalism with respect to dynamical systems	Abstract
Lünsmann, Benedict	From Effective to Physical Networks from Time Series	Abstract
Martin, Elliot	Creating and Interpreting Climate Networks: Insights and Caveats	Abstract
Marín, Arlex	Genuine cross-correlations: Which surrogate based measure reproduces analytical results best?	Abstract
Nitzan, Mor	Revealing cross talk between distant RNAs in regulatory networks	Abstract
Olguín, Paola	Stationary pattern and dynamical aspects of the functional network extracted from sleep EEGs of healthy subjects	Abstract
Pal, Pinaki	Gluing bifurcation in Rayleigh-Benard convection	Abstract
Palmigiano, Agostina	Routing information in networks at the edge of synchrony	Abstract
Pascual-García, Alberto	Inference of ecological networks from high-throughput experiments	Abstract
Pereda, Ernesto	Maximal information coefficient reveals network correlates to the perception of binaural beats	Abstract
Pidde, Aleksandra	canceled
Porz, Stephan	Pros and cons of reducing the influence of common sources on phase-based estimates of interaction-strengths	Abstract
Priesemann, Viola	Organization principles of neural activity in vivo - beyond self-organized criticality	Abstract
Rubido, Nicolas	Exact detection of direct links in networks of interacting dynamical systems	Abstract
Rubido, Nicolas	Resiliently evolving supply-demand networks	Abstract
Ríos Herrera, Wady Alexander	The influence of EEG references on the analysis of spatio-temporal interrelation pattern	Abstract
Röder, Heidelinde	Reconstructing correlation and causality between compounds of dissolved organic matter	Abstract
Rüdiger, Sten	Degree correlations in complex networks: effects on percolation and information transfer in neural populations	Abstract
Soriano Fradera, Jordi	Multi-neuron Calcium Imaging: Exploring Neuronal Dynamics in Cortical Cultures	Abstract
Srivastava, Shambhavi	Functional representation of DNA	Abstract
Tapia, Luis	Resting state of the brain and networks metrics	Abstract
Teller Amado, Sara	Dynamics in Clustered Neuronal Networks	Abstract
Valencia, Miguel	Subthalamic activity during motor state levodopa-induced transitions in Parkinson's disease	Abstract
Vasudevan, Kris	Insight into earthquake sequencing: A graph theoretic approach to modified Markov chain model	Abstract
Vasudevan, Kris	Synchronization studies: Kuramoto model on directed graphs	Abstract
Wahl, Benjamin	Definition of a nonlinear Granger causality index within the framework of stationary Fokker-Planck equations	Abstract
Wan, Xiaogeng	The causal inference of cortical neural networks during music improvisations	Abstract
Wejer, Dorota	Entropic measures of fluctuations of heart period intervals and systolic blood pressure for recordings obtained from the head-up tilt table test	Abstract
Wilting, Jens	Time-resolved inference of interaction properties of coupled dynamical systems	Abstract

Generating mechanisms of Extreme Events in Oscillator Networks Ansmann, Gerrit (University of Bonn, Universitätsklinikum Bonn, Epileptology, Bonn, Germany)

We investigate the dynamical behavior of networks of FitzHugh--Nagumo oscillators which exhibits rare and irregular events of unusually high amplitude (extreme events). Similar events, such as earth quakes, rogue waves, harmful algal blooms, and epileptic seizures are of high relevance in natural dynamical systems. We demonstrate that extreme events can occurr for different network topologies and report on precursors and generating mechanisms for these events. (Supported by the Volkswagen Foundation (Grant Nos. 85388 and 85392))

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Instability of genetic networks to internal perturbations Bajic, Djordje (Centro Nacional de Biotecnologia , Systems Biology Program, Madrid, Spain)

Genetic networks constitute a map of phenotypically relevant interactions among components of a biological system. So far, these networks have been implicitly considered as a rather "static" picture, and it is largely unknown to what extent and how do they change in response to internal or external perturbation (e.g. environmental change or genetic perturbation). We used flux balance analysis to characterize the instability of genetic networks to gene deletions in a model metabolic system. We found instability to be strongly influenced by specific functional contexts, notably, those displaying high degrees of functional degeneracy. Moreover, these architectures are linked to environment-unspecific functions, such as core catabolic pathways. As a consequence, instability of genetic networks in response to neutral deletion accumulation strongly predicts the associated loss genetic and environmental robustness.

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Signature of Genre Specific Musical Creativity on Cortical Network Patterns: A Pilot Study Bhattacharya, Joydeep (University of London, Goldsmiths College, Department of Psychology, London, United Kingdom)

Ernesto Pereda1, Shama Rahman2, Joydeep Bhattacharya3 1Department of Industrial Engineering, University of La Laguna, La Laguna, Tenerife, Spain 2Department of Mathematics, Imperial College London, London, United Kingdom 3Department of Psychology, Goldsmiths, University of London, London, United Kingdom Creativity is the pinnacle of complex human cognition, yet the network characteristics of human brain in creative action are least understood. Studying musical creativity offers a unique opportunity, as it allows investigating brain dynamics during creative performance. Classical music and jazz are the two main genres of music in the Western world and are often associated with different forms of creativity. Therefore, the main objective of this pilot study was to characterise cortical network patterns associated with genre specific musical creativity. We recorded electrical activities (EEG) of eight professional pianists while they were engaged with creative musical tasks equally on musical extracts from both genres (10 for each genre). For four standard EEG frequency bands, theta (4-8 Hz), alpha (8-16 Hz), beta (16-30 Hz), and gamma (30- 50 Hz), bivariate phase synchronization values were calculated by phase locking value (PLV), and subsequently were used as the strengths of links in an adjacency matrix forming a connected network. We further calculated three network measures: strength, clustering and efficiency, at both local (the node) and global (the network) level. Additionally, we also studied the sensitivity of these measures across different thresholds of the links in the adjacency matrix. At the global level, we found significant differences, robust across different thresholds, between the two types of musical excerpts, and the effects were largest for the beta frequency band. The overall cortical network was found to be more synchronised, efficient and integrated during classical improvisation as compared to jazz improvisation. Locally these differences were manifested over fronto-central brain regions, with a clear right hemispheric lateralization. This pilot study provides the first evidence of the association between genre specific musical creativity and cortical network.

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Data-driven prediction of extreme events in high-dimensional excitable systems Bialonski, Stephan (Max Planck Institute for the Physics of Complex Systems, Dresden, Germany)

Extreme events can occur in very different dynamical systems, ranging from nature to society and technology. Due to the, often severe, consequences of these extreme events, their reliable and successful prediction is highly desirable. We study extreme events in a network of FitzHugh-Nagumo units. This deterministic system shows events which are rare, short-lasting, recurrent, and propagate through the network. To predict such events, we present an approach which does not rely upon equations of motions but on time series of observables of the system and on the coupling topology of the network. By iterative predictions, we are able to forecast the onset of an extreme event as well as the propagation and extinction of excitation, i.e. the full life-cycle of an extreme event.

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Information based approach for data analysis and network inference Bianco-Martinez, Ezequiel (University of Aberdeen, Institute for Complex Systems and Mathematical Biology (ICSMB), Natural and Computing Science, Aberdeen, United Kingdom)

The study of information exchanged between nodes of complex networks is of primordial importance for understanding its structure and functionality. We use Mutual Information Rate (MIR) to quantify the exchange of information per unit of time between pairs of nodes in systems that posses decay of correlation. We present novel results about the robustness of MIR to infer structural,functional and causal connectivity in complex networks emerging from dynamical maps and neural models.

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Network Dynamics as an Inverse Problem: Reconstruction from Time Series Casadiego Bastidas, Jose Luis (Max Planck Institute for Dynamics and Self-Organization, Network Dynamics, Göttingen, Germany)

Methods for reconstructing structural connections of networks are generally based on perturbing the network and analyzing its behavior posterior to the perturbation. However, little is known when perturbations are experimentally unfeasible. Recent findings show that structural connections may also be recovered from time series if dynamical features (e.g., local and coupling functions) are known a priori. Nonetheless, most (if not all) of these features are usually not known in experimental setups, thus, turning the reconstruction problem into a difficult task to solve. Here we show that the structural connectivity of a network may be directly retrieved from time series alone if the reconstruction problem is posed in terms of subspaces of interactions. When properly constructed, these subspaces reliably map structural connections. Moreover, we found that long time series and compositions of several different short time series yield identical results. This suggests that the mechanism revealing connections is the sampling of the state-space. Our approach is model-independent, this ensures its generality and applicability among network models and makes it especially suitable when dynamical features and perturbations are unknown or unfeasible.

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Amplitude death and lag synchronization in coupled oscillators: a common mechanism Dana, Syamal (CSIR-Indian Institute of Chemical Biolgy, Kolkata, India)

We report a delay effect in amplitude death or oscillation death of two coupled oscillators for a large parameter mismatch under diffuisve coupling. In particular, we find that the coupled oscillators, due to the parameter mismatch, develop a time shift or delay via an emergent generalized-lag synchronization and ceases to oscillate for a characteristic delay at a critical coupling. This is similar to amplitude death in two identical oscillators for a critical coupling delay. We present experimental as well as numerical evidence using examples of the chaotic Chua oscillator and the Bonhoeffer-van der Pol limit cycle oscillator. Further we confirm that the lag synchronization is a common mechanism of death for other different form of coupling: conjugate coupling, repulsive coupling, nonlinear coupling.

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Amplitude death and oscillation death in coupled dynamical system: Mechanisms of transition Dana, Syamal (CSIR-Indian Institute of Chemical Biolgy, Kolkata, India)

Amplitude death (AD) is well known emergent behavior of coupled oscillators. AD is mainly reported in coupled systems under parameter mismatch or delay in coupling interaction. Several other coupling forms are also able to induce death in both limit cycle and chaotic oscillators. Oscillation death (OD) is another kind of cessation of oscillation which was also observed in many coupled systems. AD and OD are now clearly distinguished as stable homogeneous steady state (HSS) and stable inhomogeneous steady state (IHSS) respectively. In a HSS state, the coupled oscillators are stabilized to one unique equilibrium point whereas in the case of IHSS, the individual systems populate separate stable steady states. The study of these quenched states has important practical consequences. The HSS for example is a desirable goal for control of instabilities in various physical systems such as lasers, and its robustness is an important criterion for a stable ground state in a healthy cell signaling network. On the other hand, the IHSS has useful applications in biological systems e.g. in representing cell differentiation, diversity of stable states in coupled genetic oscillators, survival of species. We report emergence of both kinds of death scenario when we add a repulsive link to a synchronized set of two identical oscillators and vary the coupling strength, HSS and IHSS in coupled oscillators, limit cycle and chaotic oscillator. Interestingly, we find [1-2] a transition from a HSS to IHSS with varying coupling strength. This phenomenon is reported simultaneously by others [3-5] but in diffusive coupled oscillators under parameter mismatch. They explained this transition as an effect of parameter perturbation that induces a pitchfork bifurcation (PB) similar to the Turing type symmetry breaking instabilities in a medium. On the other hand, we find the transition due to addition of repulsive interaction. However, besides the PB in limit cycle oscillators, we find diverse routes of transition [2]. Particularly, in coupled chaotic oscillators, we find two additional routes of transition, transcritical bifurcation and saddle-node bifurcation. Further, we extended our results to a network of identical oscillators which are synchronized under diffusive coupling where we assume that a repulsive link may evolve due to local disturbance: fault in a power-grid, local awareness campaign in a population network under the threat of a spreading epidemic, inhibitive coupling link in a cell signaling network. In practical sense, the repulsive link can have destructive effect such as a power-grid black-out due to a local fault and alternatively, a constructive effect in curving a spreading of an epidemic by the local or global awareness campaign. The repulsive link is modeled as an averaging effect of mutual interactions between two neighboring oscillators and act as a negative feedback link to the local oscillators. The number of repulsive links is assumed to grow in time in a network of oscillators when the death scenario emerges above a critical number of repulsive links. We find [1] that a fewer repulsive links than the size of the network suffice to induce the death oscillation in the network. We observed HSS and its transition to IHSS in globally coupled network of oscillators (using both limit cycle and chaotic models) as a resultant effect of repulsive interaction and its strength. [1] C. R. Hens, P. Pal, O. I. Olusola, S. K. Dana, Phys. Rev. E 88, 034902 (2013). [2] C. R. Hens, P. Pal, S.K.Bhowmick, P.K.Roy, A.Sen, S. K. Dana, PRE 89 (2014). in Press. [3] A. Koseska, E. Volkov, J. Kurths, Phys. Rev. Letts. 111, 024103 (2013). [4] W. Zou, D. V. Senthilkumar, A. Koseska, J. Kurths, Phys. Rev. E 88, 050901 (2013). [5] A.Koseska, E. Volkov, J. Kurths, Phys. Rep. 531 (4), 173 (2013).

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The effect of graded and categorical feedback on learning related global synchronization Di Bernardi Luft, Caroline (Goldsmiths, University of London, Department of Psychology, London, United Kingdom)

Feedback is crucial for learning and it comes in different forms, from sensory signals to more sophisticated verbal feedback. In order to learn from feedback, the brain has to implement a series of operations that require both local and global interactions between multiple brain regions. In this study, we demonstrated how both nondirected (Weighted Phase Lag Index: WPLI - Vinck et al., 2011 ) and directed (Phase Slope Index: PSI – Nolte et al., 2008) synchronization methods can be used to investigate feedback-guided learning. We conducted two EEG experiments using a time estimation task, in which the participants were required to estimate a time interval of 1.7 s. After each response, the participants received feedback, which consisted of finely graded (difference between the participant's estimation and the target - Experiment 1) or categorical ('too fast', 'correct', 'too slow' - Experiment 2) feedback. For graded feedback, we found an increase in WPLI values only in the beta frequency band (17-24 Hz) between mid-frontal electrodes (peak at FCz) and central contralateral (peak at C3) immediately following the feedback (Luft et al., 2014). For categorical feedback, we found the effect only in the theta frequency band (4-8 Hz) and the directed connectivity, as measured by PSI, from mid-frontal to central contralateral electrodes increased in the immediate period following the feedback; the directed connectivity from mid-frontal to pre-frontal electrodes (peak at F5) was observed at later stages (Luft et al., 2013). Importantly, the connectivity patterns found in both studies were consistently correlated with performance and were significantly more pronounced in the high-learners (i.e. participants who learnt better with feedback). Altogether these studies suggest that the underlying brain connectivity patterns reflect general cognitive operations used for processing feedback.

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Measuring delay directed interactions with symbolic transfer entropy Dickten, Henning (University of Bonn, Medical Center, Dept. of Epileptology, Bonn, Germany)

We investigate whether delayed directed interactions between coupled dynamical systems can be identified with an extension of symbolic transfer entropy. Using time series from paradigmatic model systems we show pros and cons of our method. We present an application of our approach to identify delayed directed interactions between brain regions using multi-channel electroencephalographic recordings from epilepsy patients. This work was supported by the Deutsche Forschungsgemeinschaft (Grant No: LE 660/5-2)

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A dynamic network analysis of space weather activity as observed in multiple ground based magnetometer stations Dods, Joe (University of Warwick, Physics, Coventry, United Kingdom)

Joe Dods(1) and Sandra Chapman(1,2) 1 Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, U.K. 2 Max Planck Institute for the Physics of Complex Systems, Dresden, Germany Space weather is the response of the Earths geomagnetic environment to changes in the solar and solar wind driving. At earth this generates geomagnetic storms and substorms which can be seen in magnetic field perturbations and in auroral activity. We investigate whether these observations can be characterised in terms of networks, which would provide a tool to quantify the impact of space weather events. These magnetic field perturbations are detected by chains of spatially distributed magnetometer stations in the auroral regions. SuperMAG is a new database containing magnetometer data at a cadence of 1min from 100s stations situated across the globe, which we use to form a dynamical network of space weather activity. The power spectral density of magnetometer data during a substorm is broadband and the substorms themselves are transient in nature and highly variable, existing for ~30min to ~few hours. We will discuss the optimal choices of frequency bands, window length, thresholds and lag ranges in relation to the cross-correlation used to form the adjacency matrix. We check the robustness of our results by constructing psuedo-random timeseries from the data and recalculating the networks. The dynamical network parameters can be compared to images of the aurora taken by the Ultraviolet Imager (UVI) on the POLAR satellite which images the dynamics of the aurora from above. This establishes the link between the network dynamics and energy dissipation seen in the aurora.

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Network Inference in the Presence of Latent Confounders Elsegai, Heba (University of Aberdeen, Institute of Complex System and Mathematical Biology, Mathematical Sciences , Aberdeen, United Kingdom)

Detecting causal interactions in multivariate systems, in terms of Granger-causality, is of major interest in many areas of research. In applications, it is often impossible to observe all components of the system. Missing certain components of the system under study can lead to spurious interactions to appear. In this study, we provide evidence that in some cases the “true” network structure of the investigated system can be inferred even in the case of incomplete observation of important processes. The standard renormalised partial directed coherence (rPDC) method is used as a means to detect Granger-causal interactions. This method is complemented by analysing the (partial) covariance matrix of residual noise process to detect instantaneous, spurious interactions. Sub-network analyses are performed to infer the true network structure of the underlying system. Our novel approach demonstrates to what extent inference of unobserved processes is feasible.

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Non-Linear Dynamics of Learning and its Application to Colour Identification Gascoyne, Daniel (Loughborough University, Physics, leicester, United Kingdom)

As a contrasting approach to the Neural Network description of learning we present a dynamical system modelled by differential equations capable of performing the primary tasks of artificial intelligence (classification, retention, recognition). This work draws upon the concepts introduced by Janson [arXiv:1107.0674 (2011)]. The system shapes it phase velocity vector field in response to the received inputs, classifying stimuli in an un-supervised manner. Recognition of stimuli occurs in parallel to class formation. A 3-dimensional phase velocity vector field is utilized to demonstrate the systems response to stimuli received from a web-camera. The model is shown to be able to classify and recognize colours using the RGB colour classification system.

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Is the epileptic focus the most important region in epileptic brain networks? Geier, Christian (University of Bonn, Germany, Medical Center, Department of Epileptology, Bonn, Germany)

We investigate whether the brain region responsible for the generation of epileptic seizures -- the epileptic focus -- represents the most important node in an epileptic brain network. We apply a data-driven method to derive functional brain networks from intra-cranial multi-channel electroencephalographic data recorded from patients with focal epilepsies. We characterize the importance of sampled brain regions in a time-resolved manner with different centrality metrics and assess significance with surrogate networks. We will show under which circumstances the epileptic focus can be regarded as most important for various observable network dynamics. Supported by the Deutsche Forschungsgemeinschaft (Grant No: LE 660/4-2)

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Predicting and triggering long jumps and sticks in molecular diffusion Hallerberg, Sarah (MPIDS Göttingen, Network Dynamics, Göttingen, Germany)

Authors: S. Hallerberg and A. S. de Wijn Diffusion can be strongly affected by the appearance of ballistic flights (long jumps) as well as long-lived sticking trajectories (long sticks). Using statistical inference techniques, we investigate the appearance of long jumps and sticks in molecular-dynamics simulations of diffusion in a prototype system, a benzene molecule on a graphite substrate. We find that specific fluctuations in certain, but not all, internal degrees of freedom of the molecule can be linked to the occurrence of either long jumps or sticks. Furthermore, we show that by changing the prevalence of these predictors with an outside influence, the diffusion of the molecule can be controlled. The approach presented in this proof of concept study is very generic, and can be applied to larger and more complex molecules. Additionally, the predictor variables can be chosen in a general way so as to be accessible in experiments, making the method feasible for control of diffusion in applications. From a conceptual point of view, we use statistical inference in combination with ROC-curves as a simplified framework for testingfor Granger causality in point processes. Our results also demonstrate that data-mining techniques can be used to investigate the phase-space structure of high-dimensional nonlinear dynamical systems.

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Chimera state in globally coupled chaotic oscillators. Hens, Chittaranjan (Council of Scientific and Industrial Research, Indian Institute of Chemical Biology, Central Instrumentation, Kolkata, India)

Recently, it is reported that coexisting populations of synchronized and desynchronized oscillators can emerge in a network of globally coupled complex Ginzburg-Landau system We extend the result here to chaotic systems with numerical examples and try to understand the mechanism behind it.

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Extreme Multistability in network of oscillators. Hens, Chittaranjan (Council of Scientific and Industrial Research, Indian Institute of Chemical Biology, Central Instrumentation, Kolkata, India)

We report here extreme multistability (coexistence of large number of attaractors)in network of chaotic oscillators. We have used nonlinear global coupling which is based on Lyapunov function stability and linear coupling in a closed ring to generate extreme multistability.

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High-order interactions between words in written language Hernandez Lahme, Damian Gabriel (Instituto Balseiro and Centro Atomico Bariloche, CNEA and CONICET, Centro Atómico Bariloche, The Statistical and Interdisciplinary Physics Group, Bariloche, Argentina)

Words not only present long correlations but also interact within groups of words in a way that can not be explained only by pairwise dependencies. In this work we study these interactions within triplets of words analyzing their distributions across a text. To quantify this effect, we apply a method based on maximum entropy techniques, measuring how the entropy reduces if three-point dependencies are considered.

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Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information Hlinka, Jaroslav (Academy of Sciences of the Czech Republic, Institute of Computer Science, Department of Nonlinear Dynamics and Complex Systems, Prague, Czech Republic)

Across geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information exchange between the nodes. For geophysical systems such as global climate, these relations are commonly not theoretically known but estimated from recorded data using causality analysis methods. These include bivariate nonlinear methods based on information theory and their linear counterpart. The trade-off between the valuable sensitivity of nonlinear methods to more general interactions and the potentially higher numerical reliability of linear methods may affect inference regarding structure and variability of climate networks. We investigate the reliability of directed climate networks detected by selected methods and parameter settings, using a stationarized model of dimensionality-reduced surface air temperature data from reanalysis of 60-year global climate records. Overall, all studied bivariate causality methods provided reproducible estimates of climate causality networks, with the linear approximation showing higher reliability than the investigated nonlinear methods. On the example dataset, optimizing the investigated nonlinear methods with respect to reliability increased the similarity of the detected networks to their linear counterparts, supporting the particular hypothesis of the near-linearity of the surface air temperature reanalysis data.

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Granger causality estimate of information flow in temperature fields is consistent with wind direction Jajcay, Nikola (Academy of Sciences of the Czech Republic, Institute of Computer Science, Department of Nonlinear Dynamics and Complex Systems, Prague, Czech Republic)

authors: Nikola Jajcay (1,2), Jaroslav Hlinka (1), David Hartman (1), and Milan Paluš (1) affiliations: (1) Department of Nonlinear Dynamics and Complex Systems, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic (2) Department of Meteorology and Environment Protection, Charles University in Prague, Prague, Czech Republic Granger causality analysis is designed to quantify whether one time series is useful in forecasting another. We apply the time domain Granger causality analysis based on autoregressive processes to gridded daily surface air temperature data. For each grid-point pair, the direction and strength of the causal influence were computed with the one-day lag, effectively assessing the direction of the information flow in the temperature field. In order to remove the influence of different distances of the grid-points in the original angularly regular grid of the NCEP/NCAR reanalysis, the data were transformed into an equidistant geodesic grid of 642 grid points. The strongest causalities have been found in the Northern Hemisphere’s extratropics, where the temperature information is flowing eastward, in agreement with the prevailing westerlies. In contrast, only weak causalities have been observed in the tropics, which may be arising from higher spatio-temporal homogeneity. In the second step, we quantitatively compared this estimate of information flow with the actual wind directions from NCEP/NCAR reanalysis data transformed onto the equidistant geodesic grid of 642 points. This was done for the surface layer and for the 850, 700, 500, 300 and 100hPa layers. The direction of the information flow matches the flow of the air masses, particularly well in the Northern Hemisphere’s extratropics, i.e. for the strongest causalities. This agreement holds throughout the troposphere, slightly increasing with the height up to 500hPa level, then remains the same until bottom stratosphere. The agreement between the information flow in the air temperature field and the flow of air masses suggests the Granger causality as a suitable tools for constructing directed climate networks.

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Cluster Explosive Synchronization in Complex Networks Ji, Peng (PIK, RD IV, Potsdam, Germany)

The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter we demonstrate that the nodes in a second- order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call cluster explosive synchronization. We provide a rigorous analytical treatment using a mean-field analysis in uncorrelated networks. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

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Extreme events and network failures Kishore, Vimal (Indian Institute of Science Education and Research, Theoretical Physics, Pune, India)

Events like traffic jams, floods, and power blackouts are not uncommon. Inspired by such events, we study extreme events on complex networks. In this poster, I will discuss the random walk on network and associated extreme events taking place on networks. We will also propose a model to study network failures based on extreme events and discuss the nature of such failures.

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Rényi transfer entropy and its application for intraday financial data Korbel, Jan (Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Prague, Czech Republic)

Measuring information transfer between time series is a challenging task. Classical statistical approaches, usually based on correlations, do not provide complete image about sources of the information flow. On the other hand, there have been introduced many sophisticated approaches that enable to reveal the complex nature of many processes. One of these successful approaches is based on transfer entropy, introduced by Schreiber [1] and generalized to the class of $q$-Rényi transfer entropies by Kleinert et. al. [2]. The latter one enables to investigate the different parts of underlying distribution, by changing the key parameter $q$ such that it 'zooms' different part of distribution. The whole concept of transfer entropy enables to reveal not only strength of information flow, but also the direction. The concept of Rényi entropy is then applied to intraday financial data of largest stock exchange indices, in order to observe, how are information flows among exchanges changed during the day. Individual stock markets exhibit different activity during the day, and the shift between particular opening hours results of varying information flow during the day. These findings provide an important part for understanding such complex systems, and can serve to practitioners and financial traders for optimizing their activities.

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Information flow/transfer: a rigorous formalism with respect to dynamical systems Liang, X. San (Nanjing Institute of Meteorology, School of Marine Sciences, Nanjing, China, People's Republic of)

Information flow, or information transfer as may be referred to, is a fundamental notion in general physics which has wide applications in scientific disciplines. Recently, a rigorous formalism has been established with respect to both deterministic and stochastic systems, with flow measures explicitly obtained. These measures possess some important properties, among which is flow or transfer asymmetry. The formalism has been validated and put to application with a variety of benchmark systems such as the baker transformation, Henon map, truncated Burgers-Hopf system, Langevin equation, etc. In the chaotic Burgers-Hopf system, all the transfers, save for one, are essentially zero, indicating that the processes underlying a dynamical phenomenon, albeit complex, could be simple. (Truth is simple.) In the Langevin equation case, it is found that there could be no information flowing from one certain time series to another series, though the two are highly correlated. Information flow/transfer provides a quantitative measure of the cause-effect relation between dynamical events, a relation usually hidden behind the correlation in a traditional sense.

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From Effective to Physical Networks from Time Series Lünsmann, Benedict (MPI Dynamic and Self organization, Non-Linear Dynamics, Network Dynamics, Göttingen, Germany)

How can we reconstruct network connectivity from recorded time series? So far, many methods have been developed to infer the effective connectivity of deterministic and noisy systems (e.g. neural, gene regulatory or protein-protein interaction networks) using statistical dependencies of the nodes' time series under the assumption of stationary states, i.e. with a time-invariant joint probability distribution for a system’s variables. Often, such statistical measures are thresholded or otherwise discretized and the resulting network interpreted as the systems’ interactions. Yet, resulting reconstruction errors are not yet known. Here we address this problem for generic linear and weakly nonlinear dynamical systems and reveal the quality of reconstruction connected to regular, random and intermediate network topologies. We show that the quality of reconstruction depends crucially on the network's topology, and in particular that its behavior cannot be captured by the mean degree or the mean clustering coefficient. Evaluating receiver operator characteristic (ROC) curves, we quantify how reconstruction depends on structural network characteristics. We reveal that thresholding of statistical dependency measures is only suited to reconstruct networks from dynamics if their topology are close to regular such that intrinsically complex topologies cannot be reliably detected.

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Creating and Interpreting Climate Networks: Insights and Caveats Martin, Elliot (University of Calgary, Physics and Astronomy, Calgary, Canada)

Climate networks have received much attention in recent years as a tool to gain insights into climate dynamics. An important interpretation of these findings was that parts of the globe act in correlated relationships which become weaker, on average, during El Niño periods. We have found that this result is sensitive to parameters such as time lags and the precise definition of El Niño events. Contrary to previous findings we show that El Niño periods actually exhibit higher correlations then “Normal” climate conditions, while still having lower correlations then La Niña periods. In addition, during the construction of these networks the time delay between nodes is often misestimated. This is due to properties of a commonly used cross-correlation estimator. For non-stationary signals the time series is often partitioned into smaller sections that individually can be presumed to be stationary. In order for there to be sufficient statistics what is commonly done is use a sliding time window of fixed length to calculate the cross-correlation at different lags, whereas the traditional method is sliding the time series against each other and having increasingly smaller windows for larger time lags. The time delay between signals can then be taken as the one at which the correlation is maximal. We show that doing this strongly biases the time delays to extreme values in climate data, and that this is generally true for time series with long-range correlations.

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Genuine cross-correlations: Which surrogate based measure reproduces analytical results best? Marín, Arlex (Universidad Autonoma del Estado de Morelos, Faculty of Science, Computational Modelling, Cuernavaca, Mexico)

The analysis of short segments of noise-contaminated, multivariate real world data constitutes a challenge. In this paper we compare several techniques of analysis, which are supposed to correctly extract the amount of genuine cross-correlations from a multivariate data set. In order to test for the quality of their performance we derive time series from a linear test model, which allows the analytical derivation of genuine correlations. We compare the numerical estimates of the four measures with the analytical results for different correlation pattern. In the bivariate case all but one measure performs similarly well. However, in the multivariate case measures based on the eigenvalues of the equal-time cross-correlation matrix do not extract exclusively information about the amount of genuine correlations, but they rather reflect the spatial organization of the correlation pattern. This may lead to failures when interpreting the numerical results as illustrated by an application to three electroencephalographic recordings of three patients suffering from pharmacoresistent epilepsy.

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Revealing cross talk between distant RNAs in regulatory networks Nitzan, Mor (The Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem, Israel)

Competing endogenous RNAs (ceRNAs) were recently introduced as RNA transcripts that affect each other’s expression level through competition for their microRNA (miRNA) coregulators. This stems from the bidirectional effects between miRNAs and their target RNAs, where a change in the expression level of one target affects the level of the miRNA regulator, which in turn affects the level of other targets. By the same logic, miRNAs that share targets compete over binding to their common targets and therefore also exhibit ceRNA-like behavior. Taken together, perturbation effects could propagate in the posttranscriptional regulatory network through a path of coregulated targets and miRNAs that share targets, suggesting the existence of distant ceRNAs. Here we study the prevalence of distant ceRNAs and their effect in cellular networks. Analyzing the network of miRNA-target interactions deciphered experimentally in HEK293 cells, we show that it is a dense, intertwined network, suggesting that many nodes can act as distant ceRNAs of one another. Indeed, using gene expression data from a perturbation experiment, we demonstrate small, yet statistically significant, changes in gene expression caused by distant ceRNAs in that network. We further characterize the magnitude of the propagated perturbation effect and the parameters affecting it by mathematical modeling and simulations. Our results show that the magnitude of the effect depends on the generation and degradation rates of involved miRNAs and targets, their interaction rates, the distance between the ceRNAs and the topology of the network. Although demonstrated for a miRNA-mRNA regulatory network, our results offer what to our knowledge is a new view on various posttranscriptional cellular networks, expanding the concept of ceRNAs and implying possible distant cross talk within the network, with consequences for the interpretation of indirect effects of gene perturbation.

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Stationary pattern and dynamical aspects of the functional network extracted from sleep EEGs of healthy subjects Olguín, Paola (Universidad Autónoma de Morelos, Faculty of Science, Physic, Mexico, Mexico)

Scalp EEG recordings are noise contaminated and highly non-stationary. Therefore one might expect, that an average of an interrelation measure as the Pearson coefficient, which takes positive and negative values with the same probability should (almost) vanish. However, the average zero-lag cross correlation matrix estimated over the whole night of healthy subjects result in a pronounced, characteristic correlation pattern. This interrelation structure is interpreted as the fingerprint of an dynamical grounds state of the brain activity (limit cycle), necessary to maintain and coordinate vitally important processes. If this is true, dynamical aspects of the brain activity are manifested by continuous deviations from this stable structure. We propose two different techniques to evaluate quantitatively such deviations. The obtained results provide not only a more homogenous picture across subjects when compared to the total amount of correlations. Furthermore, they are consistent with the hypothesis of synaptic homeostasis.

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Gluing bifurcation in Rayleigh-Benard convection Pal, Pinaki (National Institute of Technology Durgapur, Mathematics, Durgapur, India)

Homoclinic guling bifurcation occurs in a dynamical system when a pair of limit cycles become symulteneously homoclinic to a single saddle point. It is observed in many physical as well as laboratory systems possessing special symmetries. The examples include electronic circuit systems, optothermal systems, fluid systems etc. We present the phenomenon of homoclinic gluing bifurcation in Rayleigh Benard convection (RBC) by deriving a four dimensional dynamical system. We observe logarithmic divergence of time period of oscillation of the limit cycles near the homoclinic gluing bifurcation. The pattern dynamics in the vicinity of the gluing bifurcation is also investigated. Direct numerical simulation of the three dimentional RBC is also done to validate the model results.

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Routing information in networks at the edge of synchrony Palmigiano, Agostina (Max Planck Institute for Dynamics and Self-Organization, Göttingen, Nonlinear Dynamics, Goettingen, Germany)

Agostina Palmigiano (1,2), Fred Wolf (1,2), Theo Geisel (1,2) and Demian Battaglia (2,3) 1) Max Planck Institute for Dynamics and Self Organization 2) Bernstein Center for Computational Neuroscience Goettingen 3) Institut de Neurosciences des Systèmes,Aix-Marseille Université Behavior and cognition require a dynamically reconfigurable communication scheme, flexible in scales much faster than the ones imposed by mechanisms modifying the architecture of the net- work’s structural connectivity. Processes such as attention expose that the brain can actively select specific information-flow channels in very fast time scales. A well established hypothesis known as communication through coherence [Fries, 2005], proposes oscillatory coherence as a possible gating strategy to regulate inter-areal information transmission. Recent studies, however, have challenged this view arguing that synchronous episodes in brain signals are of short duration (100 ms) [Burns, Xing, Shapley,2011] and of a drifting frequency, [Ray, Maunsell, 2010] making oscillatory coordina- tion an unreliable mechanism for information routing. In this work we aim to bring together these views in apparent contradiction. We show that in a model of a local neural circuit of randomly interconnected conductance-based neurons with hetero- geneous properties, a robust regime characterized by transient synchrony emerges. When multiple local circuits are connected by long range excitation, short-lived events of coordinated synchroniza- tion between areas occur with a self-organized frequency tracking. We show furthermore that, dur- ing these events, phase locking also transiently occurs, not necessarily in phase, but favoring phase relations reminiscent of attractors that the connected circuits would develop for stronger synchrony (”ghost attractors”)[Battaglia,Brunel,Hansel, 2007]. These phase relations in turn determine preferential directions for the information transmission as measured by Transfer entropy. In particular, effectively unidirectional communication in presence of a bidirectional connectivity can arise at the edge of developing synchrony, and the direction of transmission can be flexibly inverted. In particular, we show that this direction can be actively con- trolled by applying a weak driving bias, and even by precisely-timed synchronous pulses stimulation, showing that the resulting changes in the instantaneous phase difference distribution translate into changes of information flow within only a few oscillatory cycles, smaller than the average gamma- burst length.

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Inference of ecological networks from high-throughput experiments Pascual-García, Alberto (Consejo Superior de Investigaciones Científicas (CSIC), Centro de Biologia Molecular Severo Ochoa, Bioinformatics Unit, Madrid, Spain)

An increasing number of available data coming from high-throughput experiments has boosted our efforts for finding ecological trends, and there is an increasing evidence pointing to a qualitative similar picture between the patterns found in macro and microorganisms [1, 2]. These progresses have been possible in part thanks to the reemergence of prokaryotic biogeography, but little attention have been made to the methodological differences that microbiological data impose over classical analysis methods of taxon-sites matrices. Here we discuss null models of absence-presence and abundance matrices obtained from generalized linear methods [3], incorporating an appropriate notion of independence among species. We propose novel pairwise measures of aggregation and segregation among taxa that can be derived analytically. Since in the null model taxa do not interact, these inferred associations represent false positives of our method. This fact allow us to assess the significance of properties observed in the network inferred from observed data by comparison with respect to those properties obtained with networks constructed from the null model. The coarse grained nature of this kind of data makes difficult to conclusively reject the hypothesis stating that aggregations are due to underlying environmental preferences not considered in the null model. But a detailed analysis of these networks suggest that cooperative interactions are common and may have an important role in bacterial ecology [4]. [1] M. Claire Horner-Devine, Karen M. Carney, Brendan J. M. Bohannan, An ecological perspective on bacterial biodiversity, Proc. R. Soc. Lond. B, 2003. [2] M. Claire Horner-Devin, Melissa Lage, Jennifer B. Hughes, Brendan J. M. Bohannan, A taxa-area relationship for bacteria, Nature, 2004. [3] Navarro-Alberto, J., Manly, B., Null model analyses of presence absence matrices need a definition of independence, Population Ecology, 2009. [4] Pascual-García, A., Tamames, J., Bastolla, U. Bacteria dialog with Santa Rosalia: A critical appraisal of habitat filtering versus ecological interactions. Submitted.

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Maximal information coefficient reveals network correlates to the perception of binaural beats Pereda, Ernesto (University of La Laguna, Biomedical Techonology, Industrial Engineering, San Cristobal de La Laguna, Spain)

Maximal information coefficient (MIC), an information-theoretic measure, has recently been developed with a promising potential of application to high dimensional complex data sets (Reshef et al, 2011, Science). Further, the significance of a given MIC value depends only on the length of the data, thereby facilitating the estimation of the p-level of the correlation of each pair of time series. These features turn MIC into a suitable measure for the exploration of associations in a multidimensional neuroimage data set. In this study, we applied this index to a multivariate dataset comprising sixty-four EEG channels recorded from two groups of participants, musicians and non-musicians, during the auditory perception of binaural beats (BB, an illusory perceived beat out of the presentation of two sinusoidal tones, one to each ear, with a slight frequency mismatch); we systematically varied the frequency mismatch from 1 to 48 Hz. As a control condition, we presented same frequencies to both ears which did not elicit any perception of binaural beat (no binaural beat, NBB). As compared to non binaural beat condition, across groups we found that (i) mismatch or beat frequencies belonging to the alpha band (8-12 Hz) produced the most robust changes in the MIC values, and (ii) the number of electrode pairs showing nonlinear associations decreased gradually with increasing frequency mismatch. When the MIC values were compared between the two groups, significant differences were found for mismatch frequencies below 15 Hz and higher than 35 Hz; such differences were conspicuously absent for control or NBB condition. Altogether, these results revealed a network correlates of binaural beat perception and demonstrated the usefulness of MIC to efficiently estimate interdependences in multivariate neural data sets.

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Organization principles of neural activity in vivo - beyond self-organized criticality Priesemann, Viola (Max-Planck-Institute for Dynamics and Self-Organization, Non-linear Dynamics, Göttingen, Germany)

In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have been observed also for neural activity and thus, it has been proposed that SOC underlies brain organization, too. However, for spiking activity in vivo, evidence for SOC is still lacking. Therefore we analyzed spikes recorded in awake rats, cats and monkeys and compared these spike avalanches to avalanches from an established SOC neural model. We found fundamental differences between the spike and the model avalanches. These differences could be overcome by eliminating the separation of time scales (STS) from the SOC model, and by making the model slightly sub-critical. The same results were obtained for avalanches from local field potentials in humans. Thus neural activity is better approximated by a slightly sub-critical regime that is driven (i.e., without a STS), than by a SOC state proper. Potential advantages are faster information processing capacities due to the loss of STS, and a safety margin from super-criticality (e.g., epilepsy).

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Exact detection of direct links in networks of interacting dynamical systems Rubido, Nicolas (University of Aberdeen, Institute for Complex Systems and Mathematical Biology (ICSMB), Department of Physics, Aberdeen, United Kingdom)

The inference of an underlying network structure from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as Cross-Correlation (CC, computed in absolute value, i.e., the Pearson coefficient) and Mutual Information (MI, computed via ordinal pattern analysis [Phys. Rev. Lett. 88, 174102 (2002)]). The possible existence of a direct link between different units is, however, hindered within the time-series measurements. Here we show that when an abrupt change in the ordered set of CC or MI values exits, it is possible to infer, without errors, the underlying network structure from the time-series measurements, even in the presence of observational noise, non-identical units, and coupling heterogeneity. We find that a necessary condition for the discontinuity to occur is that the dynamics of the coupled units is partially coherent, i.e., neither complete disorder nor globally synchronous patterns are present. We critically compare the inference methods based on CC and MI, in terms of how effective, robust, and reliable they are, and conclude that, in general, MI outperforms CC in robustness and reliability. Our findings are relevant for the construction and interpretation of functional networks, such as those constructed from brain or climate data.

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Resiliently evolving supply-demand networks Rubido, Nicolas (University of Aberdeen, Institute for Complex Systems and Mathematical Biology (ICSMB), Department of Physics, Aberdeen, United Kingdom)

The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for distribution systems nowadays. In this work, by using the circuit laws of Kirchhoff and Ohm, we provide the exact capacities of the edges that an optimal supply-demand network should have to operate stably under perturbations, i.e., without overloading. The perturbations we consider are the evolution of the connecting topology, the decentralization of hub sources or sinks, and the intermittence of supplier and consumer characteristics. We analyze these conditions and the impact of our results, both on the current United Kingdom power-grid structure and on numerically generated evolving archetypal network topologies.

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The influence of EEG references on the analysis of spatio-temporal interrelation pattern Ríos Herrera, Wady Alexander (Universidad Autonoma del Estado de Morelos, Faculty of Science, Physics, Cuernavaca, Mexico)

EEG references may influence drastically the multivariate analysis of the functional brain network. Spurious correlations might be induced as well as genuine correlations destroyed, depending on the chosen reference and physiological brain state. We studied the influence of 7 popular EEG references and propose a new one. Quantitative comparison if provided by analyzing artificial data derived from theoretical models, where the true correlation pattern can be perfectly controlled. Hereby we concentrate mainly on two interrelation measures: zero-lag cross correlation and phase synchronization. We investigate possible distortions of spatial interrelationships as well as possible changes of univariate properties of the signals as e.g. the autocorrelation lengths. Finally, as a proof of principles we present an application to a sleep EEG of a healthy subject. We conclude, that the new reference scheme proposed in this study performs best.

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Reconstructing correlation and causality between compounds of dissolved organic matter Röder, Heidelinde (Carl von Ossietzky University of Oldenburg, Institute for Chemistry and Biology of the Marine Environment (ICBM), Oldenburg, Germany)

Heidelinde Röder1, Jutta Niggemann2, Thorsten Dittmar2, Gunnar Gerdts3, Ulrike Feudel1, Jan Freund1 1. Theoretical Physics/ Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, Germany. 2. Research Group for Marine Geochemistry (ICBM, Carl von Ossietzky University of Oldenburg and Max Planck Institute Bremen, Germany) 3. Alfred Wegener Institute, Helmholtz Center for Polar and Marine Research, Helgoland, Germany. We are dealing with time series containing information about relative abundance and presence of dissolved organic matter (DOM) from the German Bight (North Sea). Samples of surface water were taken over a period of two years at Helgoland with an average sampling interval of 6 days. The aim is to apply correlation and causal measures to better understand the mechanisms involved in production, degradation and transformation of these molecular compounds. Our first attempt is to group the complex set of time series by a repetitive application of k-means clustering. We found out that synchronous variation of molecular signals underlying the cluster formation reveals groups of molecules with similar molecular properties. A cross-correlation analysis between consensus time series of the detected groups and time series of biological and oceanographic factors allowed closer insights into the processes that are driving the dynamics of DOM. For causal inference we are aiming at applying linear Granger-Causality measures based on vector autoregressive processes.

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Degree correlations in complex networks: effects on percolation and information transfer in neural populations Rüdiger, Sten (Humboldt-Universität zu Berlin, Physik, Berlin, Germany)

Cognitive processes in the brain crucially depend on the network topologies of neuronal links. We here study how correlations in the degrees of neurons, defined by the numbers of synaptic connections, affect network behavior. First, we discuss percolation as a model for global response in electrically stimulated neural cultures. We show that spatial constraints generally impede percolation. However, degree correlations promote or hinder percolation depending on further factors of network construction. Second, we study networks of integrate-and-fire neurons and identify conditions for which a network reliably transmits a stimulus of given firing rate. We present a mathematical theory to calculate population firing rates from a self-consistent system of equations taking into account degree distributions and degree correlations. This method helps us to analyze the emergence of responses in networks with increasingly complex connectivity. Specifically, we show that assortative degree correlations strongly improve the sensitivity for low stimuli. Using information theory we further find an optimum in assortativity, with larger levels reducing again sensitivity for ensembles of signals.

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Multi-neuron Calcium Imaging: Exploring Neuronal Dynamics in Cortical Cultures Soriano Fradera, Jordi (University of Barcelona, Physics Faculty, Estructura i Constituents de la Matèria, Barcelona, Spain)

Elisenda Tibau1, Miguel Valencia2 and Jordi Soriano1 1 Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Barcelona, Spain 2 Centro de Investigación Médica Aplicada (CIMA). Universidad de Navarra. Navarra, Spain. Neuronal cultures are one of the most prominent examples of complex systems, and a versatile tool to model the emergence of collective phenomena in the brain. Here we report experimental studies aimed at characterizing the interplay activity-connectivity and the balance between excitatory and inhibitory circuits. Data is obtained by monitoring the spontaneous activity of a large population of neurons in rat cortical cultures using high-speed fluorescence calcium imaging. The measurements are then repeated using a gradually weaker excitatory or inhibitory connectivity. This allows a quantification of the effective connectivity of the network upon perturbation of the physical circuitry. Among other observations, we have detected communities of neurons that maintain a persistent coherent activity. The size and synchronization strength of the community depends on the balance between excitation and inhibition. We finally show that our analysis is also useful to model the degradation of activity and connectivity in neuronal tissues, as occurs for instance in neurodegenerative disorders.

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Functional representation of DNA Srivastava, Shambhavi (University of Aberdeen, Institute of Complex System and Mathematical Biology, Physics, Aberdeen, United Kingdom)

Escherichia coli, a bacteria that is present in the human digestive system is one of the commonly used model organisms: its DNA is well known, well studied, and can be used to test mathematical approaches towards modelling the DNA. In this work, we design a special encoding to represent nucleotide sequences into symbolic sequences and create a symbolic map of the E.coli DNA. This map allows for a straightforward characterisation of the DNA through informational (Shannon's source entropy and mutual information rate measures), expansion rates, and the rate of the correlation decay. We also establish functional connectivity between two regions in this symbolic space (representing two groups of similar two words) based on the rate at which information is exchanged and on the correlation strength between two regions. Interpreting a node to represent a group of similar words (a region in the symbolic space) and edges to represent the functional connections between them (measured by the rate of information exchanged or the coefficient of the correlation decay) allows us to construct a network representation of the DNA, a graph representation of the grammatical rules governing the appearance of nucleotide words.

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Resting state of the brain and networks metrics Tapia, Luis (Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin", DRCC, Campinas, Brazil)

Neuronal elements in the brain are not isolated, they work together and they work in an organized way. The functional magnetic resonance imaging (fMRI) technique allows identifying cortical networks when the brain develops a task. But even in the absence of any task, cortical brain networks are present. These networks increase their activity in the absence of a task this is the so called resting state of the brain. A consistent finding is that some brain regions with similar functionality are time correlated in resting state. So far there isn't a clear interpretation of the meaning of the resting state of the brain. One theory suggests that this state is involved in introspection and mind wandering, this includes any thoughts that are not associated with the external environment. Other theory suggests that this state is the baseline of the brain processing and information maintenance. Recent studies have modeled the brain networks architecture with aid of graph theory. The advantage of such approaches is that this theory may quantify the structure and functionality of the brain. For example, in resting state fMRI analysis, functional connectivity is a measure of how strongly any two brain regions are time correlated. From a graph theory point of view regions are considered as nodes, and time correlations are considered as links between nodes of the graph. This work presents a graph analysis of resting state data sets. Two groups of persons are analized healthy volunteers and epylepsy pacients. We divided the brain in 90 regions using the AAL (Automated Anatomical Labeling) atlas, and extracted the mean time course of each region. We compared the strength of these time course correlations between brain regions using Pearson's correlation. Defning a threshold we can classify any two time courses as correlated or not correlated. We thus obtained an undirected graph that allows us to make measures of the network and compare between the groups.

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Dynamics in Clustered Neuronal Networks Teller Amado, Sara (Universitat de Barcelona, Physics, Estructura i Constituents de la Matèria, Barcelona, Spain)

Neuronal cultures are excellent systems to study the interplay between dynamics and connectivity in neuronal networks. Although cultures show a rich repertoire of spontaneous activity, the mechanisms that relate a particular network architecture with a specific dynamic behavior are still poorly understood. Here we study spontaneous activity in a particular configuration of neuronal cultures known as 'clustered neuronal networks'. These networks are formed by interconnected neuronal assemblies called clusters that emerge naturally when the cultured neurons do not have any motility restriction in the space. We monitor the spontaneous activity of the clustered networks using calcium fluorescence imaging. The firing of the network is characterized by bursts of activity, in which the clusters are activated sequentially in a short time window, remaining silent until the next bursting episode. The analysis of the time delays between consecutive clusters within the bursts allows the reconstruction of the directed functional connectivity of the network. We find that the networks are formed such that preference in connectivity between clusters is based on the similarity between their activities, a property that is called 'assortative mixing'. Our results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture.

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Subthalamic activity during motor state levodopa-induced transitions in Parkinson's disease Valencia, Miguel (Foundation for Applied Medical Research / University of Navarra, Center for Applied Medical Research, Neurosciences, Pamplona, Spain)

Levodopa (L-DOPA) is one of the main drugs used to treat Parkinson's disease (PD). It crosses the protective blood–brain barrier and is converted to dopamine in the brain. Dopamine concentration increases and alleviates the disease's initial symptoms. As disease progresses, L-DOPA appears to become less effective in eliminating motor symptoms: motor fluctuations oscillate between "off" times, a state of decreased mobility, and "on" times, periods when the medication is working and symptoms are controlled. In some persons with PD, the "on-off" fluctuations are somewhat predictable whereas for other people, these "on-off" transitions are unpredictable. No one knows why fluctuations are unpredictable in some cases, thus warranting further investigation to understand/characterize such transitions. Oscillatory activity in local field potentials recorded in the subthalamic nucleus (STN) differs depending on whether the subject is in the “off” or in “on” motor state. In the “off” state, a marked peak of beta activity between 13 and 20 Hz is observed in most patients in the dorsal (motor) region of the nucleus, together with high-frequency activity around 250 Hz. In the “on” state, the typical “off” beta peak is absent. In the high frequency range, a peak can also be observed, but at a higher frequency (350 Hz) and with a wider distribution than its “off” equivalent. Additionally, a peak in the high gamma range (between 60 and 80 Hz) is also present in a 30% of the nuclei in this state. Although all these activities have been well characterized on each of the two motor states, little is known about the pattern of changes in the oscillatory activity during the transition between them. Here we propose to analyze the recordings obtained from 36 STN from 18 PD patients through the DBS implanted to treat their disease, during the off-on motor transition. We will use linear (harmonic analysis) and non-linear (permutation entropy) tools to study patterns of change in brain activity around the moment when the patient described to enter the “on” motor state. We expect that the results of this work will help to delve into the mechanisms that mediate in the transition between the motor states as well as into the unpredictability of these routes in some patients as the disease progresses.

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Insight into earthquake sequencing: A graph theoretic approach to modified Markov chain model Vasudevan, Kris (University of Calgary, Geoscience, Calgary, Canada)

We construct a directed graph to represent a Markov chain of global earthquake sequences and analyze the statistics of transition probabilities linked to earthquake zones. For earthquake zonation, we consider the simplified plate boundary template of Kagan, Bird, and Jackson (2010). We generalize this Markov chain of earthquake sequences by including the recurrent events in space and time for each event in the record-breaking sense. The record-breaking recurrent events provide the basis for redefining the weights for the state-to-state transition probabilities. We use a distance-dependent look-up table for each zone to assign the distance-dependent weights for the recurring events. From this modified Markov chain, we obtain a time-series of state-to-state transition probabilities. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode function. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor. (A presentation co-authored with Dr. Micahel Cavers of the Department of Mathematics and Statistics)

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Synchronization studies: Kuramoto model on directed graphs Vasudevan, Kris (University of Calgary, Geoscience, Calgary, Canada)

We analyze the Kuramoto model of weakly coupled phase oscillators on directed graphs to review their synchronization behavior. One of the challenges lies in both detecting and understanding the relationship of their geometry and the evolving dynamics. To this end, we generate directed, weighted graphs from a family of small-world undirected graphs by introducing varying degrees of asymmetry to the latter. In this present study, these graphs contain degrees of connectedness ranging from being strong to weak. Aside from looking at the classical properties of graphs to obtain information on the relationship between the structure of the digraph and its dynamics, we look at some new definitions. For a directed graph, the spectral theory leads to its Laplacian or Diplacian and degree of asymmetry. We explore the possibility of their relevance in understanding the synchronization on directed graphs. Also, we investigate the conditions under which symmetry breaking could occur in the steady-state solution of the Kuramoto model. Finally, we compare the geometrical properties and synchronization behavior of directed, weighted graphs with those of their small-world graphs.

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Definition of a nonlinear Granger causality index within the framework of stationary Fokker-Planck equations Wahl, Benjamin (University of Oldenburg, Institute for Chemistry and Biology of the Marine Environment, Theoretical Physics/Complex Systems, Oldenburg, Germany)

Time series Y Granger causes X, if the prediction of X based on the past of a set of time series that describes the whole universe is decreased by excluding Y. The concept was practically restricted to discrete linear models whereon Granger causality indices (GCI) are defined. We show that a nonlinear GCI with certain desired properties is defined on special Fokker-Planck equations. We give an example with limit cycle.

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The causal inference of cortical neural networks during music improvisations Wan, Xiaogeng (Imperial College London, Imperial College London, Mathematics, London, United Kingdom)

In this paper, we present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and "let-go"mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional mutual information from mixed embedding (MIME), to analyze directed correlations between di?erent EEG channels, which was combined with network theory to construct both intra-brain and cross-brain neural networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and "let-go"mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found musicians responding differently to listeners when playing music in different conditions.

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Entropic measures of fluctuations of heart period intervals and systolic blood pressure for recordings obtained from the head-up tilt table test Wejer, Dorota (The University of Gdańsk, Institute of Theorethical Physics and Astrophysics, Gdańsk, Poland)

The head-up tilt table test is an accepted method for provoking the activation of main cardiovascular regulatory mechanisms. The test is dynamic and therefore demands dynamical methods to measure interactions in the cardiovascular system. In particular, observation of the development of the vasovagal syncope provides valuable insights into the phenomenon of the cardiovascular regulation. Marked differences are observed in the dynamical response to the tilt test of healthy subjects prone to spontaneous fainting and those who are less susceptible to fainting.

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Time-resolved inference of interaction properties of coupled dynamical systems Wilting, Jens (Rheinische Friedrich-Wilhelms-Universität Bonn, Dept. of Epileptology, Bonn, Germany)

We investigate the problem of inferring interaction properties of coupled dynamical systems with phase based methods using an approximation of the underlying phase evolution equations in terms of a functional basis. A recently published modification (PRL todo) promises wider applicability of these methods with better time resolution and same accuracy by using Bayesian inference and knowledge propagation. We investigate the capability and limitations of this new framework. Its performance is compared to well-established least square methods at the example of well-known linear and non-linear, structurally identical or dififferent model systems. We point out that care should be taken when interpreting obtained results, as inferred information about coupling directionality and strength are misleading if the investigated dynamics are not adequately approximated by phase based methods. Tracking of time-varying coupling parameters requires a limitation of knowledge propagation. We present an improved method for the time-resolved inference of interaction properties, which obtains comparable or better accuracy without sensitive dependance upon the choice of an internal parameter of the inference algorithm as the original algorithm. We apply this new method to intracranial, multichannel EEG recordings from epilepsy patients and present time-evolving interaction properties of different communicating brain areas, which allows tracking of the dynamics of epileptic brain networks at a priorly not accessible time resolution.

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