Collective fluctuations in networks of noisy components

Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is unclear. Here we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with the system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such nontrivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure

Heterogeneity in connectivity of habitat networks saves stable coexistence of competing species

Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity and emergence of altruism in society, to name a few. Various mechanisms of coexistence including spatial structure of populations, heterogeneous individuals, and heterogeneous environments, have been proposed. In reality, individuals disperse and interact on complex networks. We examine how heterogeneous degree distributions of networks influence coexistence, focusing on models of cyclically competing species. We show analytically and numerically that heterogeneity in degree distributions promotes stable coexistence.Comment: 4 figure

Pluto’s ocean is capped by gas hydrates

Many icy solar system bodies possess subsurface oceans. At Pluto, Sputnik Planitia’s location near the equator suggests the presence of a subsurface ocean and a locally thinned ice shell. To maintain an ocean, Pluto needs to retain heat inside. On the other hand, to maintain large variations in ice shell thickness, Pluto’s ice shell needs to be cold. Achieving such an interior structure is problematic. Here we show that the presence of a thin layer of clathrate hydrates (gas hydrates) at the base of the ice shell can explain both the long-term survival of the ocean and the maintenance of shell thickness contrasts. Clathrate hydrates act as a thermal insulator, preventing the ocean from complete freezing while keeping the ice shell cold and immobile. The most likely clathrate guest gas is methane either contained in precursor bodies and/or produced by cracking of organic materials in the hot rocky core. Nitrogen molecules initially contained and/or produced later in the core would likely not be trapped as clathrate hydrates, instead supplying the nitrogen-rich surface and atmosphere. The formation of a thin clathrate hydrate layer capping a subsurface ocean may be an important generic mechanism maintaining long-lived subsurface oceans in relatively large but minimally-heated icy satellites and Kuiper Belt Objects

The Correlation of the NA Measurements by Counting 28Si Atoms

open12sìpartially_openembargoed_20160715Mana, G.; Massa, E.; Sasso, C. P.; Stock, M.; Fujii, K.; Kuramoto, N.; Mizushima, S.; Narukawa, T.; Borys, M.; Busch, I.; Nicolaus, A.; Pramann, A.Mana, Giovanni; Massa, Enrico; Sasso, CARLO PAOLO; Stock, M.; Fujii, K.; Kuramoto, N.; Mizushima, S.; Narukawa, T.; Borys, M.; Busch, I.; Nicolaus, A.; Pramann, A

Structure of Cell Networks Critically Determines Oscillation Regularity

Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously oscillatory cells. Such biological rhythms have notable periodicity despite the internal and external noise present in each cell. Previous experimental studies indicate that the regularity of oscillatory dynamics is enhanced when noisy oscillators interact and become synchronized. This effect, called the collective enhancement of temporal precision, has been studied theoretically using particular assumptions. In this study, we propose a general theoretical framework that enables us to understand the dependence of temporal precision on network parameters including size, connectivity, and coupling intensity; this effect has been poorly understood to date. Our framework is based on a phase oscillator model that is applicable to general oscillator networks with any coupling mechanism if coupling and noise are sufficiently weak. In particular, we can manage general directed and weighted networks. We quantify the precision of the activity of a single cell and the mean activity of an arbitrary subset of cells. We find that, in general undirected networks, the standard deviation of cycle-to-cycle periods scales with the system size $N$ as $1/\sqrt{N}$, but only up to a certain system size $N^*$ that depends on network parameters. Enhancement of temporal precision is ineffective when $N>N^*$. We also reveal the advantage of long-range interactions among cells to temporal precision

Competency of Education for Interntional Understanding: By analyzing Dircke Geography: For Bilingual Classes in Germany

This paper aims to clarify the characteristics of learning units on Education for International Understanding (EIU) and their structure, appropriate geographical teaching materials on EIU, streategies for competence acquisition, and perspectives of ESD within learning units on EIU by analyzing two learning units “Globalisation” and “Global Disparities” in the geography textbook for bilingual lesson ”Diercke Geography: For Bilingual Classes”. The results of the analysis showed that 1)“Globalisation” focuses on the theories of globalisation and “Global Disparities” aims to learn not only theories but also regionl images; 2) Competency is repeatedly acquired through different learning activities ; 3) “Global Disparities” is designed from the viewpoint of “think globally, act locally”

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.Comment: 9 figure