Article
The detection limit of human vision has remained unclear. Using a quantum light source capable of generating single-photon states of light, authors here report that humans can perceive a single photon incidence on the eye with a probability above chance.
Nature Communications doi: 10.1038/ncomms12172
Authors: Jonathan N. Tinsley, Maxim I. Molodtsov, Robert Prevedel, David Wartmann, Jofre Espigulé-Pons, Mattias Lauwers, Alipasha Vaziri
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the order parameter. While noise always tends to synchronize the oscillators, the coupling can act against synchrony if it is repulsive. For identical oscillators, the fully synchronous state remains stable for small enough repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion of the oscillators frequencies at synchrony.
Author(s): G. Timár, S. N. Dorogovtsev, and J. F. F. Mendes
A majority of studied models for scale-free networks have degree distributions with exponents greater than 2. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free equilibrium networks that have the degree distribution exponen…[Phys. Rev. E] Published Fri Jul 22, 2016
We investigate random sequential adsorption (RSA) on a random graph via the following greedy algorithm: Order the n vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős–Rényi random graph. We consider these generalizations in the large-graph limit \(n\rightarrow \infty \) and characterize the jamming constant, the limiting proportion of active vertices in the maximal greedy set.
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered.
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to study the existence and stability of cluster solutions. Cluster solutions are phase locked solutions where the oscillators separate into groups. Oscillators within a group are synchronized while those in different groups are phase-locked. We give model independent existence and stability results for symmetric cluster solutions. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.
Author(s): Shuchao Cao, Jun Zhang, Daniel Salden, Jian Ma, Chang'an Shi, and Ruifang Zhang
An aging population is bringing new challenges to the management of escape routes and facility design in many countries. This paper investigates pedestrian movement properties of crowd with different age compositions. Three pedestrian groups are considered: young student group, old people group, and…
[Phys. Rev. E 94, 012312] Published Thu Jul 21, 2016
Author(s): Ewan R. Colman and Nathaniel Charlton
The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting w…
[Phys. Rev. E 94, 012313] Published Thu Jul 21, 2016
Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes.
Trophic coherence, a measure of the extent to which the nodes of a directed network are organised in levels, has recently been shown to be closely related to many structural and dynamical aspects of complex systems, including graph eigenspectra, the prevalence or absence of feed-back cycles, and linear stability. Furthermore, non-trivial trophic structures have been observed in networks of neurons, species, genes, metabolites, cellular signalling, concatenated words, P2P users, and world trade. Here we consider two simple yet apparently quite different dynamical models -- one a Susceptible-Infected-Susceptible (SIS) epidemic model adapted to include complex contagion, the other an Amari-Hopfield neural network -- and show that in both cases the related spreading processes are modulated in similar ways by the trophic coherence of the underlying networks. To do this, we propose a network assembly model which can generate structures with tunable trophic coherence, limiting in either perfectly stratified networks or random graphs. We find that trophic coherence can exert a qualitative change in spreading behaviour, determining whether a pulse of activity will percolate through the entire network or remain confined to a subset of nodes, and whether such activity will quickly die out or endure indefinitely. These results could be important for our understanding of phenomena such as epidemics, rumours, shocks to ecosystems, neuronal avalanches, and many other spreading processes.
Author(s): Shogo Mizutaka and Toshihiro Tanizawa
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal network is uniquely determined by the Pearson coefficient of the d…[Phys. Rev. E] Published Thu Jul 21, 2016
The Fourth Law of Humanics
Nature 535, 7612 (2016). doi:10.1038/535460a
Author: Ian Stewart
Small steps to freedom.
Nature advance online publication 20 July 2016. doi:10.1038/nature18930
Authors: M. Omar Din, Tal Danino, Arthur Prindle, Matt Skalak, Jangir Selimkhanov, Kaitlin Allen, Ellixis Julio, Eta Atolia, Lev S. Tsimring, Sangeeta N. Bhatia & Jeff Hasty
The widespread view of bacteria as strictly pathogenic has given way to an appreciation of the prevalence of some beneficial microbes within the human body. It is perhaps inevitable that some bacteria would evolve to preferentially grow in environments that harbour disease and thus provide a natural platform for the development of engineered therapies. Such therapies could benefit from bacteria that are programmed to limit bacterial growth while continually producing and releasing cytotoxic agents in situ. Here we engineer a clinically relevant bacterium to lyse synchronously at a threshold population density and to release genetically encoded cargo. Following quorum lysis, a small number of surviving bacteria reseed the growing population, thus leading to pulsatile delivery cycles. We used microfluidic devices to characterize the engineered lysis strain and we demonstrate its potential as a drug delivery platform via co-culture with human cancer cells in vitro. As a proof of principle, we tracked the bacterial population dynamics in ectopic syngeneic colorectal tumours in mice via a luminescent reporter. The lysis strain exhibits pulsatile population dynamics in vivo, with mean bacterial luminescence that remained two orders of magnitude lower than an unmodified strain. Finally, guided by previous findings that certain bacteria can enhance the efficacy of standard therapies, we orally administered the lysis strain alone or in combination with a clinical chemotherapeutic to a syngeneic mouse transplantation model of hepatic colorectal metastases. We found that the combination of both circuit-engineered bacteria and chemotherapy leads to a notable reduction of tumour activity along with a marked survival benefit over either therapy alone. Our approach establishes a methodology for leveraging the tools of synthetic biology to exploit the natural propensity for certain bacteria to colonize disease sites.
Author(s): Alex Roxin and Albert Compte
Bistability between attracting fixed points in neuronal networks has been hypothesized to underlie persistent activity observed in several cortical areas during working memory tasks. In network models this kind of bistability arises due to strong recurrent excitation, sufficient to generate a state …
[Phys. Rev. E 94, 012410] Published Wed Jul 20, 2016
Author(s): K. Premalatha, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan
We investigate the emergence of different kinds of imperfectly synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population I and existence of solitary oscillators which escape from the …
[Phys. Rev. E 94, 012311] Published Wed Jul 20, 2016
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Science is a growing system, exhibiting ~4% annual growth in publications and ~1.8% annual growth in the number of references per publication. Combined these trends correspond to a 12-year doubling period in the total supply of references, thereby challenging traditional methods of evaluating scientific production, from researchers to institutions. Against this background, we analyzed a citation network comprised of 837 million references produced by 32.6 million publications over the period 1965-2012, allowing for a temporal analysis of the `attention economy' in science. Unlike previous studies, we analyzed the entire probability distribution of reference ages - the time difference between a citing and cited paper - thereby capturing previously overlooked trends. Over this half-century period we observe a narrowing range of attention - both classic and recent literature are being cited increasingly less, pointing to the important role of socio-technical processes. To better understand the impact of exponential growth on the underlying knowledge network we develop a network-based model, featuring the redirection of scientific attention via publications' reference lists, and validate the model against several empirical benchmarks. We then use the model to test the causal impact of real paradigm shifts, thereby providing guidance for science policy analysis. In particular, we show how perturbations to the growth rate of scientific output affects the reference age distribution and the functionality of the vast science citation network as an aid for the search & retrieval of knowledge. In order to account for the inflation of science, our study points to the need for a systemic overhaul of the counting methods used to evaluate citation impact - especially in the case of evaluating science careers, which can span several decades and thus several doubling periods.
The spatial distributions of system's frequencies have significant influences on the critical coupling strengths for amplitude death (AD) in coupled oscillators. We find that the left and right critical coupling strengths for AD have quite different relations to the increasing spatial period m of the frequency distribution in coupled oscillators. The left one has a negative linear relationship with m in log-log axis for small initial frequency mismatches while remains constant for large initial frequency mismatches. The right one is in quadratic function relation with spatial period m of the frequency distribution in log-log axis. There is an optimal spatial period m 0 of frequency distribution with which the coupled system has a minimal critical strength to transit from an AD regime to reviving oscillation. Moreover, the optimal spatial period m 0 of the frequency distribution is found to be related to the system size . Numerical examples are explored to reveal the inner regimes of effects of the spatial frequency distribution on AD.
Author(s): Philipp Schierz, Johannes Zierenberg, and Wolfhard Janke
{\color{blue} We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real microcanonical ensemble where the sum of kinetic and potential energy is kept constant. The method is t…[Phys. Rev. E] Published Fri Jul 15, 2016
This paper generalizes the stability test method via integral estimation for integer-order neutral time-delay systems to neutral fractional-delay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractional-delay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractional-delay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.
The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector - for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.
Author(s): Daniel Heger and Katharina Krischer
Uncertain recognition success, unfavorable scaling of connection complexity or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a new network architecture of coup…[Phys. Rev. E] Published Tue Jul 19, 2016
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission rates to the nodes results in the heterogeneity, which in turn causes the segregation of nodes in terms of various sub populations. The aim of the study is to gain microscopic insight into the effect of interactions among various sub populations in the spreading processes of disease over such networks. The discrete time Markov chain method based upon the susceptible infected susceptible (SIS) model of diseases transmission has been used to describe the spreading of epidemic over the networks. The study is parameterized in terms of variable $\lambda$, defined as the number of contacts a node makes with the fraction of its neighboring nodes. From the simulation results, it is found that the spread of epidemic on such networks is critical in terms of number of minimum contacts made by a node below which there is no outbreak of disease. The degree of infection in these networks is assessed from the size of epidemic defined in terms of fraction of infected nodes of the total number and their corresponding level of infection. The results of the parametric study demonstrates the dependence of the epidemic size upon number of concurrent contacts made by a node ($\lambda$ ) and the average number of links per node. In both these cases, the size of the epidemic is found to increase with the corresponding increase in respective parameters.
Collaborations and citations within scientific research grow simultaneously and interact dynamically. Modelling the coevolution between them helps to study many phenomena that can be approached only through combining citation and coauthorship data. A geometric graph for the coevolution is proposed, the mechanism of which synthetically expresses the interactive impacts of authors and papers in a geometrical way. The model is validated against a data set of papers published on PNAS during 2007-2015. The validation shows the ability to reproduce a range of features observed with citation and coauthorship data combined and separately. Particularly, in the empirical distribution of citations per author there exist two limits, in which the distribution appears as a generalized Poisson and a power-law respectively. Our model successfully reproduces the shape of the distribution, and provides an explanation for how the shape emerges via the decisions of authors. The model also captures the empirically positive correlations between the numbers of authors' papers, citations and collaborators.