Experimental demonstration of chaos in a microbial food web

Discovering why natural population densities change over time and vary with location is a central goal of ecological and evolutional disciplines. The recognition that even simple ecological systems can undergo chaotic behaviour has made chaos a topic of considerable interest among theoretical ecologists. However, there is still a lack of experimental evidence that chaotic behaviour occurs in the real world of coexisting populations in multi-species systems. Here we study the dynamics of a defined predator-prey system consisting of a bacterivorous ciliate and two bacterial prey species. The bacterial species preferred by the ciliate was the superior competitor. Experimental conditions were kept constant with continuous cultivation in a one-stage chemostat. We show that the dynamic behaviour of such a two-prey, one-predator system includes chaotic behaviour, as well as stable limit cycles and coexistence at equilibrium. Changes in the population dynamics were triggered by changes in the dilution rates of the chemostat. The observed dynamics were verified by estimating the corresponding Lyapunov exponents. Such a defined microbial food web offers a new possibility for the experimental study of deterministic chaos in real biological systems.     

Detecting deterministic dynamics of cardiac rhythm

Under the acceptable hypothesis that cardiac rhythm is an approximately deterministic process with a small scale noise component, an available way is provided to construct a model that can reflect its prominent dynamics of the deterministic component. When applied to the analysis of 19 heart rate data sets, three main findings are stated. The obtained model can reflect prominent dynamics of the deterministic component of cardiac rhythm; Cardiac chaos is stated in a reliable way; Dynamical noise plays an important role to the generation of complex cardiac rhythm.     

Period multupling-evidence for nonlinear behaviour of the canine heart

Although there has recently been considerable interest in applying the theory of nonlinear dynamics to the analysis of complex systems, as yet applications of the theory to biological systems in vivo have been very limited. We report here evidence of nonlinear behaviour in the electrocardiogram and arterial blood pressure traces of the noradrenaline-treated dog. Noradrenaline produces variations in these traces that repeat themselves with regular periods of integral numbers of heart-beats (period multupling), an effect that resembles the 'period-doubling' and other 'bifurcative' behaviour observed when the driving frequency of a nonlinear oscillator is increased above a critical value. The simplest type of periodic variation that we report is the so-called 'electrical alternans', which has long been known as one response of cardiac electrical activity to certain stresses and disease states.     

The effect of aggressiveness on the population dynamics of a territorial bird

A central issue in ecology lies in identifying the importance of resources, natural enemies and behaviour in the regulation of animal populations. Much of the debate on this subject has focused on animals that show cyclic fluctuations in abundance. However, there is still disagreement about the role of extrinsic (food, parasites or predators) and intrinsic (behaviour) factors in causing cycles. Recent studies have examined the impact of natural enemies, although spatial patterns resulting from restricted dispersal or recruitment are increasingly recognized as having the potential to influence unstable population dynamics. We tested the hypothesis that population cycles in a territorial bird, red grouse Lagopus lagopus scoticus, are caused by delayed density-dependent changes in the aggressiveness and spacing behaviour of males. Here we show that increasing aggressiveness experimentally for a short period in autumn reduced recruitment and subsequent breeding density by 50%, and changed population trajectories from increasing to declining. Intrinsic processes can therefore have fundamental effects on population dynamics.     

A bottom-up approach to gene regulation

The ability to construct synthetic gene networks enables experimental investigations of deliberately simplified systems that can be compared to qualitative and quantitative models. If simple, well-characterized modules can be coupled together into more complex networks with behaviour that can be predicted from that of the individual components, we may begin to build an understanding of cellular regulatory processes from the 'bottom up'. Here we have engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli. We studied its behaviour in synthetic gene networks under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. We develop a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and show that the model can be extended and used to accurately predict the in vivo behaviour of the network when it is expanded to include positive feedback. The model also reveals the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which we confirm experimentally. This work shows that the properties of regulatory subsystems can be used to predict the behaviour of larger, more complex regulatory networks, and that this bottom-up approach can provide insights into gene regulation.     

High-amplitude fluctuations and alternative dynamical states of midges in Lake Myvatn

Complex dynamics are often shown by simple ecological models and have been clearly demonstrated in laboratory and natural systems. Yet many classes of theoretically possible dynamics are still poorly documented in nature. Here we study long-term time-series data of a midge, Tanytarsus gracilentus (Diptera: Chironomidae), in Lake Myvatn, Iceland. The midge undergoes density fluctuations of almost six orders of magnitude. Rather than regular cycles, however, these fluctuations have irregular periods of 4-7 years, indicating complex dynamics. We fit three consumer-resource models capable of qualitatively distinct dynamics to the data. Of these, the best-fitting model shows alternative dynamical states in the absence of environmental variability; depending on the initial midge densities, the model shows either fluctuations around a fixed point or high-amplitude cycles. This explains the observed complex population dynamics: high-amplitude but irregular fluctuations occur because stochastic variability causes the dynamics to switch between domains of attraction to the alternative states. In the model, the amplitude of fluctuations depends strongly on minute resource subsidies into the midge habitat. These resource subsidies may be sensitive to human-caused changes in the hydrology of the lake, with human impacts such as dredging leading to higher-amplitude fluctuations. Tanytarsus gracilentus is a key component of the Myvatn ecosystem, representing two-thirds of the secondary productivity of the lake and providing vital food resources to fish and to breeding bird populations. Therefore the high-amplitude, irregular fluctuations in midge densities generated by alternative dynamical states dominate much of the ecology of the lake.     

Efficient quantum computing using coherent photon conversion

Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting systems with extremely strong intrinsic nonlinearities. Furthermore, exploiting higher-order nonlinearities with multiple pump fields yields a mechanism for multiparty mediation of the complex, coherent dynamics.     

一族非线性映射及其浑沌抑制

给出了一族非线性映射,研究了优劣民用 非线性动力学系统的长期行为,揭示了该族非线性映射存在的两种运动行为：确定性运动和确定性浑沌,通过变换数值算法的途径改变局部映射,得到了一族抑制确定性浑沌产生的映射,该映射不仅保持了与原有映射相同的确定性运动,而且消除了原映射存在的确定性浑沌,将此方法应用到生物物种繁殖动力学中,可对一种生物物种的浑沌繁殖起到抑制作用。     

A test of general relativity from the three-dimensional orbital geometry of a binary pulsar.

Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the rate of orbital decay of two pulsars have been shown to be consistent with the emission of gravitational waves as predicted by general relativity, but independent verification was not possible. Such verification can in principle be obtained by determining the orbital inclination in a binary pulsar system using only classical geometrical constraints. This would permit a measurement of the expected retardation of the pulse signal arising from the general relativistic curvature of space-time in the vicinity of the companion object (the 'Shapiro delay'). Here we report high-precision radio observations of the binary millisecond pulsar PSR J0437-4715, which establish the three-dimensional structure of its orbit. We see the Shapiro delay predicted by general relativity, and we determine the mass of the neutron star and its white dwarf companion. The determination of such masses is necessary in order to understand the origin and evolution of neutron stars.     

Local interactions predict large-scale pattern in empirically derived cellular automata.

An important unanswered question in ecology is whether processes such as species interactions that occur at a local scale can generate large-scale patterns seen in nature. Because of the complexity of natural ecosystems, developing an adequate theoretical framework to scale up local processes has been challenging. Models of complex systems can produce a wide array of outcomes; therefore, model parameter values must be constrained by empirical information to usefully narrow the range of predicted behaviour. Under some conditions, spatially explicit models of locally interacting objects (for example, cells, sand grains, car drivers, or organisms), variously termed cellular automata or interacting particle models, can self-organize to develop complex spatial and temporal patterning at larger scales in the absence of any externally imposed pattern. When these models are based on transition probabilities of moving between ecological states at a local level, relatively complex versions of these models can be linked readily to empirical information on ecosystem dynamics. Here, I show that an empirically derived cellular automaton model of a rocky intertidal mussel bed based on local interactions correctly predicts large-scale spatial patterns observed in nature.     

Spatial cooperativity in soft glassy flows

Amorphous glassy materials of diverse nature-concentrated emulsions, granular materials, pastes, molecular glasses-display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications. A general feature of such systems, well documented yet not really understood, is the strongly nonlinear nature of the flow rule relating stresses and strain rates. Here we use a microfluidic velocimetry technique to characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughnesses. We find evidence for finite-size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast to the classical nonlinearities of the rheological behaviour of amorphous materials, we show that a rather simple non-local flow rule can account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of cooperativity within the flow at these scales, that is unobservable in the liquid state (lower emulsion concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers (for example, coatings), these non-locality and cooperativity effects have parallels in the behaviour of other glassy, jammed and granular systems, suggesting a possible fundamental universality.     

The dynamics of measles in sub-Saharan Africa

Although vaccination has almost eliminated measles in parts of the world, the disease remains a major killer in some high birth rate countries of the Sahel. On the basis of measles dynamics for industrialized countries, high birth rate regions should experience regular annual epidemics. Here, however, we show that measles epidemics in Niger are highly episodic, particularly in the capital Niamey. Models demonstrate that this variability arises from powerful seasonality in transmission-generating high amplitude epidemics-within the chaotic domain of deterministic dynamics. In practice, this leads to frequent stochastic fadeouts, interspersed with irregular, large epidemics. A metapopulation model illustrates how increased vaccine coverage, but still below the local elimination threshold, could lead to increasingly variable major outbreaks in highly seasonally forced contexts. Such erratic dynamics emphasize the importance both of control strategies that address build-up of susceptible individuals and efforts to mitigate the impact of large outbreaks when they occur.     

Controlled growth factor release from synthetic extracellular matrices

Polymeric matrices can be used to grow new tissues and organs, and the delivery of growth factors from these matrices is one method to regenerate tissues. A problem with engineering tissues that exist in a mechanically dynamic environment, such as bone, muscle and blood vessels, is that most drug delivery systems have been designed to operate under static conditions. We thought that polymeric matrices, which release growth factors in response to mechanical signals, might provide a new approach to guide tissue formation in mechanically stressed environments. Critical design features for this type of system include the ability to undergo repeated deformation, and a reversible binding of the protein growth factors to polymeric matrices to allow for responses to repeated stimuli. Here we report a model delivery system that can respond to mechanical signalling and upregulate the release of a growth factor to promote blood vessel formation. This approach may find a number of applications, including regeneration and engineering of new tissues and more general drug-delivery applications.     

Multifractal mass exponent spectrum of complex physiological time series

Physiological signal belongs to the kind of nonstationary and time-variant ones. Thus, the nonlinear analysis methods may be better to disclose its characteristics and mechanisms. There have been plenty of evidences that physiological signal generated by complex self-regulated system may have a fractal structure. In this work, we introduce a new measure to characterize multifractality, the mass exponent spectrum curvature, which can disclose the complexity of fractal structure from total bending degree of the spectrum. This parameter represents the nonlinear superpositions of the discrepancies of fractal dimension from all adjacent points in the curve and therefore solves the problem of original parameters for not fully reflecting the information of entire subsets in the fractal structure. The evaluations of deterministic fractal system Cantor measure validate that it is completely effective in exploring the complexity of chaotic series, and is also not affected by nonstability of the signal as well as disturbances of the noises. We then apply it to the analysis of human heart rate variability (HRV) signals and sleep electroencephalogram (EEG) signals. The experimental results show that this method can be better to discriminate cohorts under different physiological and pathological conditions. Compared with the indicator of singularity spectrum width, there are some improvements both on the computing efficiency and accuracy. Such conclusion may provide some valuable information for clinical diagnoses.     

Positive feedbacks promote power-law clustering of Kalahari vegetation

The concept of local-scale interactions driving large-scale pattern formation has been supported by numerical simulations, which have demonstrated that simple rules of interaction are capable of reproducing patterns observed in nature. These models of self-organization suggest that characteristic patterns should exist across a broad range of environmental conditions provided that local interactions do indeed dominate the development of community structure. Readily available observations that could be used to support these theoretical expectations, however, have lacked sufficient spatial extent or the necessary diversity of environmental conditions to confirm the model predictions. We use high-resolution satellite imagery to document the prevalence of self-organized vegetation patterns across a regional rainfall gradient in southern Africa, where percent tree cover ranges from 65% to 4%. Through the application of a cellular automata model, we find that the observed power-law distributions of tree canopy cluster sizes can arise from the interacting effects of global-scale resource constraints (that is, water availability) and local-scale facilitation. Positive local feedbacks result in power-law distributions without entailing threshold behaviour commonly associated with criticality. Our observations provide a framework for integrating a diverse suite of previous studies that have addressed either mean wet season rainfall or landscape-scale soil moisture variability as controls on the structural dynamics of arid and semi-arid ecosystems.     

A Self-Organizing Controller for Dynamic Processes Using Wavelet Networks

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A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes

Surface deformation in volcanic areas usually indicates movement of magma or hydrothermal fluids at depth. Stratovolcanoes tend to exhibit a complex relationship between deformation and eruptive behaviour. The characteristically long time spans between such eruptions requires a long time series of observations to determine whether deformation without an eruption is common at a given edifice. Such studies, however, are logistically difficult to carry out in most volcanic arcs, as these tend to be remote regions with large numbers of volcanoes (hundreds to even thousands). Here we present a satellite-based interferometric synthetic aperture radar (InSAR) survey of the remote central Andes volcanic arc, a region formed by subduction of the Nazca oceanic plate beneath continental South America. Spanning the years 1992 to 2000, our survey reveals the background level of activity of about 900 volcanoes, 50 of which have been classified as potentially active. We find four centres of broad (tens of kilometres wide), roughly axisymmetric surface deformation. None of these centres are at volcanoes currently classified as potentially active, although two lie within about 10 km of volcanoes with known activity. Source depths inferred from the patterns of deformation lie between 5 and 17 km. In contrast to the four new sources found, we do not observe any deformation associated with recent eruptions of Lascar, Chile.     

Symmetry perception in an insect

Symmetrical visual patterns have a salient status in human perception, as evinced by their prevalent occurrence in art, and also in animal perception, where they may be an indicator of phenotypic and genotypic quality. Symmetry perception has been demonstrated in humans, birds, dolphins and apes. Here we show that bees trained to discriminate bilaterally symmetrical from non-symmetrical patterns learn the task and transfer it appropriately to novel stimuli, thus demonstrating a capacity to detect and generalize symmetry or asymmetry. We conclude that bees, and possibly flower-visiting insects in general, can acquire a generalized preference towards symmetrical or, alternatively, asymmetrical patterns depending on experience, and that symmetry detection is preformed or can be learned as perceptual category by insects, because it can be extracted as an independent visual pattern feature. Bees show a predisposition for learning and generalized symmetry because, if trained to it, they choose it more frequently, come closer to and hover longer in front of the novel symmetrical stimuli than the bees trained for asymmetry do for the novel asymmetrical stimuli. Thus, even organisms with comparatively small nervous systems can generalize about symmetry, and favour symmetrical over asymmetrical patterns.