We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on–off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

How effective are governmental incentives to achieve widespread vaccination coverage so as to prevent epidemic outbreak? The answer largely depends on the complex interplay among the type of incentive, individual behavioral responses, and the intrinsic epidemic dynamics. By incorporating evolutionary games into epidemic dynamics, we investigate the effects of two types of incentives strategies: partial-subsidy policy in which certain fraction of the cost of vaccination is offset, and free-subsidy policy in which donees are randomly selected and vaccinated at no cost. Through mean-field analysis and computations, we find that, under the partial-subsidy policy, the vaccination coverage depends monotonically on the sensitivity of individuals to payoff difference, but the dependence is non-monotonous for the free-subsidy policy. Due to the role models of the donees for relatively irrational individuals and the unchanged strategies of the donees for rational individuals, the free-subsidy policy can in general lead to higher vaccination coverage. Our findings indicate that any disease-control policy should be exercised with extreme care: its success depends on the complex interplay among the intrinsic mathematical rules of epidemic spreading, governmental policies, and behavioral responses of individuals.

A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of “basic instinct” of an individual to determine its movement at any time step. That is, an individual is more likely to move when the local habitat becomes hostile and is no longer favorable for survival and growth. We show that, when such local habitat suitability is taken into account, robust coexistence can emerge even in the high-mobility regime where extinction is certain in the RMF model. A surprising finding is that coexistence is accompanied by the occurrence of substantial empty space in the system. Reexamination of the RMF model confirms the necessity and the important role of empty space in coexistence. Our study implies that adaptation/movements according to local habitat suitability are a fundamental factor to promote species coexistence and, consequently, biodiversity.

Background: Microalgae are promising feedstock for production of lipids, sugars, bioactive compounds and in particular biofuels, yet development of sensitive and reliable phylotyping strategies for microalgae has been hindered by the paucity of phylogenetically closely-related finished genomes.

Results: Using the oleaginous eustigmatophyte Nannochloropsis as a model, we assessed current intragenus phylotyping strategies by producing the complete plastid (pt) and mitochondrial (mt) genomes of seven strains from six Nannochloropsis species. Genes on the pt and mt genomes have been highly conserved in content, size and order, strongly negatively selected and evolving at a rate 33% and 66% of nuclear genomes respectively. Pt genome diversification was driven by asymmetric evolution of two inverted repeats (IRa and IRb): psbV and clpC in IRb are highly conserved whereas their counterparts in IRa exhibit three lineage-associated types of structural polymorphism via duplication or disruption of whole or partial genes. In the mt genomes, however, a single evolution hotspot varies in copy-number of a 3.5 Kb-long, cox1-harboring repeat. The organelle markers (e.g., cox1, cox2, psbA, rbcL and rrn16_mt) and nuclear markers (e.g., ITS2 and 18S) that are widely used for phylogenetic analysis obtained a divergent phylogeny for the seven strains, largely due to low SNP density. A new strategy for intragenus phylotyping of microalgae was thus proposed that includes (i) twelve sequence markers that are of higher sensitivity than ITS2 for interspecies phylogenetic analysis, (ii) multi-locus sequence typing based on rps11_mt-nad4, rps3_mt and cox2-rrn16_mt for intraspecies phylogenetic reconstruction and (iii) several SSR loci for identification of strains within a given species.

Conclusion: This first comprehensive dataset of organelle genomes for a microalgal genus enabled exhaustive assessment and searches of all candidate phylogenetic markers on the organelle genomes. A new strategy for intragenus phylotyping of microalgae was proposed which might be generally applicable to other microalgal genera and should serve as a valuable tool in the expanding algal biotechnology industry.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

Major progress has been made in the past decade towards understanding of the biosynthesis of red carotenoid astaxanthin and its roles in stress response while exploiting microalgae-based astaxanthin as a potent antioxidant for human health and as a coloring agent for aquaculture applications. In this review, astaxanthin-producing green microalgae are briefly summarized with Haematococcus pluvialis and Chlorella zofingiensis recognized to be the most popular astaxanthin-producers. Two distinct pathways for astaxanthin synthesis along with associated cellular, physiological, and biochemical changes are elucidated using H. pluvialis and C. zofingiensis as the model systems. Interactions between astaxanthin biosynthesis and photosynthesis, fatty acid biosynthesis and enzymatic defense systems are described in the context of multiple lines of defense mechanisms working in concert against photooxidative stress. Major pros and cons of mass cultivation of H. pluvialis and C. zofingiensis in phototrophic, heterotrophic, and mixotrophic culture modes are analyzed. Recent progress in genetic engineering of plants and microalgae for astaxanthin production is presented. Future advancement in microalgal astaxanthin research will depend largely on genome sequencing of H pluvialis and C. zofingiensis and genetic toolbox development. Continuous effort along the heterotrophic-phototrophic culture mode could lead to major expansion of the micro algal astaxanthin industry.

Nitrogen availability and cell density each affects growth and cellular astaxanthin content of Haematococcus pluvialis, but possible combined effects of these two factors on the content and productivity of astaxanthin, especially under outdoor culture conditions, is less understood. In this study, the effects of the initial biomass densities IBDs of 0.1, 0.5, 0.8, 1.5, 2.7, 3.5, and 5.0 g L-1 DW and initial nitrogen concentrations of 0, 4.4, 8.8, and 17.6 mM nitrate on growth and cellular astaxanthin content of H. pluvialis Flotow K-0084 were investigated in outdoor glass column photobioreactors in a batch culture mode. A low IBD of 0.1 g L-1 DW led to photo-bleaching of the culture within 1-2 days. When the IBD was 0.5 g L-1 and above, the rate at which the increase in biomass density and the astaxanthin content on a per cell basis was higher at lower IBD. When the IBD was optimal (i.e., 0.8 g L-1), the maximum astaxanthin content of 3.8% of DW was obtained in the absence of nitrogen, whereas the maximum astaxanthin productivity of 16.0 mg L-1 d(-1) was obtained in the same IBD culture containing 4.4 mM nitrogen. The strategies for achieving maximum Haematococcus biomass productivity and for maximum cellular astaxanthin content are discussed.

Evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuous-time data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.