Multiscale evolving complex network model of functional connectivity in neuronal cultures

Cultures of cortical neurons grown on multielectrode arrays exhibit spontaneous, robust and recurrent patterns of highly synchronous activity called bursts. These bursts play a crucial role in the development and topological selforganization of neuronal networks. Thus, understanding the evolution of synchrony within these bursts could give insight into network growth and the functional processes involved in learning and memory. Functional connectivity networks can be constructed by observing patterns of synchrony that evolve during bursts. To capture this evolution, a modelling approach is adopted using a framework of emergent evolving complex networks and, through taking advantage of the multiple time scales of the system, aims to show the importance of sequential and ordered synchronization in network function.

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

Chaos in high performance digital robot controllers

Active robot force control requires some form of dynamic inner loop control for stability. The author considers the implementation of position-based inner loop control on an industrial robot fitted with encoders only. It is shown that high gain velocity feedback for such a robot, which is effectively stationary when in contact with a stiff environment, involves problems beyond the usual caveats on the effects of unknown environment stiffness. It is shown that it is possible for the controlled joint to become chaotic at very low velocities if encoder edge timing data are used for velocity measurement. The results obtained indicate that there is a lower limit on controlled velocity when encoders are the only means of joint measurement. This lower limit to speed is determined by the desired amount of loop gain, which is itself determined by the severity of the nonlinearities present in the drive system.

Probabilistic evaluation of time series models : a comparison of several approaches

Several methods are examined which allow to produce forecasts for time series in the form of probability assignments. The necessary concepts are presented, addressing questions such as how to assess the performance of a probabilistic forecast. A particular class of models, cluster weighted models (CWMs), is given particular attention. CWMs, originally proposed for deterministic forecasts, can be employed for probabilistic forecasting with little modification. Two examples are presented. The first involves estimating the state of (numerically simulated) dynamical systems from noise corrupted measurements, a problem also known as filtering. There is an optimal solution to this problem, called the optimal filter, to which the considered time series models are compared. (The optimal filter requires the dynamical equations to be known.) In the second example, we aim at forecasting the chaotic oscillations of an experimental bronze spring system. Both examples demonstrate that the considered time series models, and especially the CWMs, provide useful probabilistic information about the underlying dynamical relations. In particular, they provide more than just an approximation to the conditional mean.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

The trilogy of John of God

Monteiro’s assertion of the almighty auteur, after the post-structuralist and post-modern experiences, which had shattered the author and his work in theory and practice, reinstates an authority aimed at organising the chaos caused by the lack of narrative. In a way, therefore, Monteiro’s output is conservative, displaying a peculiar atemporal style, which seems entirely immune to fashion. On the other hand, however, few contemporary films could be more radical than his. Authorship, in his case, means the absence of limits and total freedom of expressing his obsessive world.

Extensivity of two-dimensional turbulence

This study is concerned with how the attractor dimension of the two-dimensional Navier–Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

Dynamical complexity in a mean-field model of human EEG

A recently proposed mean-field theory of mammalian cortex rhythmogenesis describes the salient features of electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations (Liley et al 2002). This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness (Bojak & Liley 2007) and the changes in EEG spectral power associated with general anesthetic effect (Bojak & Liley 2005). From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, various routes to chaos, fat fractals and rich bifurcation scenarios occur for physiologically relevant parameter values (van Veen & Liley 2006). The origin and the character of this complex behaviour, and its relevance for EEG activity will be illustrated. The existence of short-lived unstable brain states will also be discussed in terms of the available theoretical and experimental results. A perspective on future analysis will conclude the presentation.

Mechanism for synchronized motion between two humans in mutual tapping experiments: Transition from alternative mode to synchronization mode

We performed mutual tapping experiments between two humans to investigate the conditions required for synchronized motion. A transition from an alternative mode to a synchronization mode was discovered under the same conditions when a subject changed from a reactive mode to an anticipation mode in single tapping experiments. Experimental results suggest that the cycle time for each tapping motion is tuned by a proportional control that is based on synchronization errors and cycle time errors. As the tapping frequency increases, the mathematical model based on the feedback control in the sensory-motor closed loop predicts a discrete mode transition as the gain factors of the proportional control decease. The conditions of the synchronization were shown as a consequence of the coupled dynamics based on the subsequent feedback loop in the sensory-motor system.

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Towards a resolution of ‘the paradox of the plankton’: a brief overview of the proposed mechanisms

In plankton ecology, it is a fundamental question as to how a large number of competing phytoplankton species coexist in marine ecosystems under a seemingly-limited variety of resources. This ever-green question was first proposed by Hutchinson [Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat. 95, 137–145] as ‘the paradox of the plankton’. Starting from Hutchinson [Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat. 95, 137–145], over more than four decades several investigators have put forward varieties of mechanisms for the extreme diversity of phytoplankton species. In this article, within the boundary of our knowledge, we review the literature of the proposed solutions and give a brief overview of the mechanisms proposed so far. The proposed mechanisms that we discuss mainly include spatial and temporal heterogeneity in physical and biological environment, externally imposed or self-generated spatial segregation, horizontal mesoscale turbulence of ocean characterized by coherent vortices, oscillation and chaos generated by several internal and external causes, stable coexistence and compensatory dynamics under fluctuating temperature in resource competition, and finally the role of toxin-producing phytoplankton in maintaining the coexistence and biodiversity of the overall plankton population that we have proposed recently. We find that, although the different mechanisms proposed so far is potentially applicable to specific ecosystems, a universally accepted theory for explaining plankton diversity in natural waters is still an unachieved goal.

The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.

Competing effects of toxin-producing phytoplankton on overall plankton populations in the Bay of Bengal

The coexistence of a large number of phytoplankton species on a seemingly limited variety of resources is a classical problem in ecology, known as ‘the paradox of the plankton’. Strong fluctuations in species abundance due to the external factors or competitive interactions leading to oscillations, chaos and short-term equilibria have been cited so far to explain multi-species coexistence and biodiversity of phytoplankton. However, none of the explanations has been universally accepted. The qualitative view and statistical analysis of our field data establish two distinct roles of toxin-producing phytoplankton (TPP): toxin allelopathy weakens the interspecific competition among phytoplankton groups and the inhibition due to ingestion of toxic substances reduces the abundance of the grazer zooplankton. Structuring the overall plankton population as a combination of nontoxic phytoplankton (NTP), toxic phytoplankton, and zooplankton, here we offer a novel solution to the plankton paradox governed by the activity of TPP. We demonstrate our findings through qualitative analysis of our sample data followed by analysis of a mathematical model.

Modulation of event-related desynchronization during kinematic and kinetic hand movements

Background Event-related desynchronization/synchronization (ERD/ERS) is a relative power decrease/increase of electroencephalogram (EEG) in a specific frequency band during physical motor execution and mental motor imagery, thus it is widely used for the brain-computer interface (BCI) purpose. However what the ERD really reflects and its frequency band specific role have not been agreed and are under investigation. Understanding the underlying mechanism which causes a significant ERD would be crucial to improve the reliability of the ERD-based BCI. We systematically investigated the relationship between conditions of actual repetitive hand movements and resulting ERD. Methods Eleven healthy young participants were asked to close/open their right hand repetitively at three different speeds (Hold, 1/3 Hz, and 1 Hz) and four distinct motor loads (0, 2, 10, and 15 kgf). In each condition, participants repeated 20 experimental trials, each of which consisted of rest (8–10 s), preparation (1 s) and task (6 s) periods. Under the Hold condition, participants were instructed to keep clenching their hand (i.e., isometric contraction) during the task period. Throughout the experiment, EEG signals were recorded from left and right motor areas for offline data analysis. We obtained time courses of EEG power spectrum to discuss the modulation of mu and beta-ERD/ERS due to the task conditions. Results We confirmed salient mu-ERD (8–13 Hz) and slightly weak beta-ERD (14–30 Hz) on both hemispheres during repetitive hand grasping movements. According to a 3 × 4 ANOVA (speed × motor load), both mu and beta-ERD during the task period were significantly weakened under the Hold condition, whereas no significant difference in the kinetics levels and interaction effect was observed. Conclusions This study investigates the effect of changes in kinematics and kinetics on resulting ERD during repetitive hand grasping movements. The experimental results suggest that the strength of ERD may reflect the time differentiation of hand postures in motor planning process or the variation of proprioception resulting from hand movements, rather than the motor command generated in the down stream, which recruits a group of motor neurons.