Network-based forecasting of climate phenomena.

Network theory, as emerging from complex systems science, can provide critical predictive power for mitigating the global warming crisis and other societal challenges. Here we discuss the main differences of this approach to classical numerical modeling and highlight several cases where the network approach substantially improved the prediction of high-impact phenomena: 1) El Niño events, 2) droughts in the central Amazon, 3) extreme rainfall in the eastern Central Andes, 4) the Indian summer monsoon, and 5) extreme stratospheric polar vortex states that influence the occurrence of wintertime cold spells in northern Eurasia. In this perspective, we argue that network-based approaches can gainfully complement numerical modeling.

Complexity-based approach for El Niño magnitude forecasting before the spring predictability barrier.

The El Niño Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. Early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the "spring predictability barrier" remains a great challenge for long-lead-time (over 6 mo) forecasting. To overcome this barrier, here we develop an analysis tool, System Sample Entropy (SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Niño 3.4 region. When applying this tool to several near-surface air temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Niño and the previous calendar year's SysSampEn (complexity). We show that this correlation allows us to forecast the magnitude of an El Niño with a prediction horizon of 1 y and high accuracy (i.e., root-mean-square error = 0.23° C for the average of the individual datasets forecasts). For the 2018 El Niño event, our method forecasted a weak El Niño with a magnitude of 1.11±0.23° C. Our framework presented here not only facilitates long-term forecasting of the El Niño magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.

Corrigendum: Superstatistical model of bacterial DNA architecture.

This corrects the article DOI: 10.1038/srep43034.

Statistical significance of seasonal warming/cooling trends.

The question whether a seasonal climate trend (e.g., the increase of summer temperatures in Antarctica in the last decades) is of anthropogenic or natural origin is of great importance for mitigation and adaption measures alike. The conventional significance analysis assumes that (i) the seasonal climate trends can be quantified by linear regression, (ii) the different seasonal records can be treated as independent records, and (iii) the persistence in each of these seasonal records can be characterized by short-term memory described by an autoregressive process of first order. Here we show that assumption ii is not valid, due to strong intraannual correlations by which different seasons are correlated. We also show that, even in the absence of correlations, for Gaussian white noise, the conventional analysis leads to a strong overestimation of the significance of the seasonal trends, because multiple testing has not been taken into account. In addition, when the data exhibit long-term memory (which is the case in most climate records), assumption iii leads to a further overestimation of the trend significance. Combining Monte Carlo simulations with the Holm-Bonferroni method, we demonstrate how to obtain reliable estimates of the significance of the seasonal climate trends in long-term correlated records. For an illustration, we apply our method to representative temperature records from West Antarctica, which is one of the fastest-warming places on Earth and belongs to the crucial tipping elements in the Earth system.

Superstatistical model of bacterial DNA architecture.

Understanding the physical principles that govern the complex DNA structural organization as well as its mechanical and thermodynamical properties is essential for the advancement in both life sciences and genetic engineering. Recently we have discovered that the complex DNA organization is explicitly reflected in the arrangement of nucleotides depicted by the universal power law tailed internucleotide interval distribution that is valid for complete genomes of various prokaryotic and eukaryotic organisms. Here we suggest a superstatistical model that represents a long DNA molecule by a series of consecutive ~150 bp DNA segments with the alternation of the local nucleotide composition between segments exhibiting long-range correlations. We show that the superstatistical model and the corresponding DNA generation algorithm explicitly reproduce the laws governing the empirical nucleotide arrangement properties of the DNA sequences for various global GC contents and optimal living temperatures. Finally, we discuss the relevance of our model in terms of the DNA mechanical properties. As an outlook, we focus on finding the DNA sequences that encode a given protein while simultaneously reproducing the nucleotide arrangement laws observed from empirical genomes, that may be of interest in the optimization of genetic engineering of long DNA molecules.

Scale-dependent diffusion anisotropy in nanoporous silicon.

Nanoporous silicon produced by electrochemical etching of highly B-doped p-type silicon wafers can be prepared with tubular pores imbedded in a silicon matrix. Such materials have found many technological applications and provide a useful model system for studying phase transitions under confinement. This paper reports a joint experimental and simulation study of diffusion in such materials, covering displacements from molecular dimensions up to tens of micrometers with carefully selected probe molecules. In addition to mass transfer through the channels, diffusion (at much smaller rates) is also found to occur in directions perpendicular to the channels, thus providing clear evidence of connectivity. With increasing displacements, propagation in both axial and transversal directions is progressively retarded, suggesting a scale-dependent, hierarchical distribution of transport resistances ("constrictions" in the channels) and of shortcuts (connecting "bridges") between adjacent channels. The experimental evidence from these studies is confirmed by molecular dynamics (MD) simulation in the range of atomistic displacements and rationalized with a simple model of statistically distributed "constrictions" and "bridges" for displacements in the micrometer range via dynamic Monte Carlo (DMC) simulation. Both ranges are demonstrated to be mutually transferrable by DMC simulations based on the pore space topology determined by electron tomography.

Increase of the Antarctic Sea Ice Extent is highly significant only in the Ross Sea.

In the context of global warming, the question of why Antarctic sea ice extent (SIE) has increased is one of the most fundamental unsolved mysteries. Although many mechanisms have been proposed, it is still unclear whether the increasing trend is anthropogenically originated or only caused by internal natural variability. In this study, we employ a new method where the underlying natural persistence in the Antarctic SIE can be correctly accounted for. We find that the Antarctic SIE is not simply short-term persistent as assumed in the standard significance analysis, but actually characterized by a combination of both short- and long-term persistence. By generating surrogate data with the same persistence properties, the SIE trends over Antarctica (as well as five sub-regions) are evaluated using Monte-Carlo simulations. It is found that the SIE trends over most sub-regions of Antarctica are not statistically significant. Only the SIE over Ross Sea has experienced a highly significant increasing trend (p = 0.008) which cannot be explained by natural variability. Influenced by the positive SIE trend over Ross Sea, the SIE over the entire Antarctica also increased over the past decades, but the trend is only at the edge of being significant (p = 0.034).

Long-Range Memory in Literary Texts: On the Universal Clustering of the Rare Words.

A fundamental problem in linguistics is how literary texts can be quantified mathematically. It is well known that the frequency of a (rare) word in a text is roughly inverse proportional to its rank (Zipf's law). Here we address the complementary question, if also the rhythm of the text, characterized by the arrangement of the rare words in the text, can be quantified mathematically in a similar basic way. To this end, we consider representative classic single-authored texts from England/Ireland, France, Germany, China, and Japan. In each text, we classify each word by its rank. We focus on the rare words with ranks above some threshold Q and study the lengths of the (return) intervals between them. We find that for all texts considered, the probability SQ(r) that the length of an interval exceeds r, follows a perfect Weibull-function, SQ(r) = exp(-b(ß)rß), with ß around 0.7. The return intervals themselves are arranged in a long-range correlated self-similar fashion, where the autocorrelation function CQ(s) of the intervals follows a power law, CQ(s) ∼ s-γ, with an exponent γ between 0.14 and 0.48. We show that these features lead to a pronounced clustering of the rare words in the text.

Statistical prediction of protein structural, localization and functional properties by the analysis of its fragment mass distributions after proteolytic cleavage.

Structural, localization and functional properties of unknown proteins are often being predicted from their primary polypeptide chains using sequence alignment with already characterized proteins and consequent molecular modeling. Here we suggest an approach to predict various structural and structure-associated properties of proteins directly from the mass distributions of their proteolytic cleavage fragments. For amino-acid-specific cleavages, the distributions of fragment masses are determined by the distributions of inter-amino-acid intervals in the protein, that in turn apparently reflect its structural and structure-related features. Large-scale computer simulations revealed that for transmembrane proteins, either α-helical or ß -barrel secondary structure could be predicted with about 90% accuracy after thermolysin cleavage. Moreover, 3/4 intrinsically disordered proteins could be correctly distinguished from proteins with fixed three-dimensional structure belonging to all four SCOP structural classes by combining 3-4 different cleavages. Additionally, in some cases the protein cellular localization (cytosolic or membrane-associated) and its host organism (Firmicute or Proteobacteria) could be predicted with around 80% accuracy. In contrast to cytosolic proteins, for membrane-associated proteins exhibiting specific structural conformations, their monotopic or transmembrane localization and functional group (ATP-binding, transporters, sensors and so on) could be also predicted with high accuracy and particular robustness against missing cleavages.

Significance of trends in long-term correlated records.

We study the distribution P(x;α,L) of the relative trend x in long-term correlated records of length L that are characterized by a Hurst exponent α between 0.5 and 1.5. The relative trend x is the ratio between the strength of the trend Δ in the record measured by linear regression and the standard deviation σ around the regression line. We consider L between 400 and 2200, which is the typical length scale of monthly local and annual reconstructed global climate records. Extending previous work by Lennartz and Bunde [S. Lennartz and A. Bunde, Phys. Rev. E 84, 021129 (2011)] we show explicitly that x follows the Student's t distribution P∝[1+(x/a)2/l]-(l+1)/2, where the scaling parameter a depends on both L and α, while the effective length l depends, for α below 1.15, only on the record length L. From P we can derive an analytical expression for the trend significance S(x;α,L)=∫(-x)xP(x';α,L)dx' and the border lines of the 95% significance interval. We show that the results are nearly independent of the distribution of the data in the record, holding for Gaussian data as well as for highly skewed non-Gaussian data. For an application, we use our methodology to estimate the significance of central west Antarctic warming.

Universal internucleotide statistics in full genomes: a footprint of the DNA structure and packaging?

Uncovering the fundamental laws that govern the complex DNA structural organization remains challenging and is largely based upon reconstructions from the primary nucleotide sequences. Here we investigate the distributions of the internucleotide intervals and their persistence properties in complete genomes of various organisms from Archaea and Bacteria to H. Sapiens aiming to reveal the manifestation of the universal DNA architecture. We find that in all considered organisms the internucleotide interval distributions exhibit the same [Formula: see text]-exponential form. While in prokaryotes a single [Formula: see text]-exponential function makes the best fit, in eukaryotes the PDF contains additionally a second [Formula: see text]-exponential, which in the human genome makes a perfect approximation over nearly 10 decades. We suggest that this functional form is a footprint of the heterogeneous DNA structure, where the first [Formula: see text]-exponential reflects the universal helical pitch that appears both in pro- and eukaryotic DNA, while the second [Formula: see text]-exponential is a specific marker of the large-scale eukaryotic DNA organization.

Structural and functional properties of spatially embedded scale-free networks.

Scale-free networks have been studied mostly as non-spatially embedded systems. However, in many realistic cases, they are spatially embedded and these constraints should be considered. Here, we study the structural and functional properties of a model of scale-free (SF) spatially embedded networks. In our model, both the degree and the length of links follow power law distributions as found in many real networks. We show that not all SF networks can be embedded in space and that the largest degree of a node in the network is usually smaller than in nonembedded SF networks. Moreover, the spatial constraints (each node has only few neighboring nodes) introduce degree-degree anticorrelations (disassortativity) since two high degree nodes cannot stay close in space. We also find significant effects of space embedding on the hopping distances (chemical distance) and the vulnerability of the networks.

Very early warning of next El Niño.

The most important driver of climate variability is the El Niño Southern Oscillation, which can trigger disasters in various parts of the globe. Despite its importance, conventional forecasting is still limited to 6 mo ahead. Recently, we developed an approach based on network analysis, which allows projection of an El Niño event about 1 y ahead. Here we show that our method correctly predicted the absence of El Niño events in 2012 and 2013 and now announce that our approach indicated (in September 2013 already) the return of El Niño in late 2014 with a 3-in-4 likelihood. We also discuss the relevance of the next El Niño to the question of global warming and the present hiatus in the global mean surface temperature.

Universal behavior of the interoccurrence times between losses in financial markets: independence of the time resolution.

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution P(Q)(r) of the interoccurrence times r between losses below a negative threshold -Q, for fixed mean interoccurrence times R(Q) in multiples of the corresponding time resolutions, can be described on all time scales by the same q exponentials, P(Q)(r)∝1/{[1+(q-1)ßr](1/(q-1))}. We propose that the asset- and time-scale-independent analytic form of P(Q)(r) can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution P(Q)(r) as well as the autocorrelation C(Q)(s) of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the q-exponential form of P(Q)(r) and the power-law decay of C(Q)(s).

Improved El Nino forecasting by cooperativity detection.

Although anomalous episodic warming of the eastern equatorial Pacific, dubbed El Niño by Peruvian fishermen, has major (and occasionally devastating) impacts around the globe, robust forecasting is still limited to about 6 mo ahead. A significant extension of the prewarning time would be instrumental for avoiding some of the worst damages such as harvest failures in developing countries. Here we introduce a unique avenue toward El Niño prediction based on network methods, inspecting emerging teleconnections. Our approach starts from the evidence that a large-scale cooperative mode--linking the El Niño basin (equatorial Pacific corridor) and the rest of the ocean--builds up in the calendar year before the warming event. On this basis, we can develop an efficient 12-mo forecasting scheme, i.e., achieve some doubling of the early-warning period. Our method is based on high-quality observational data available since 1950 and yields hit rates above 0.5, whereas false-alarm rates are below 0.1.

Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints.

We consider Erdö]s-Rényi-type networks embedded in one-dimensional (de=1) and two-dimensional (de=2) Euclidean space with the link-length distribution p(r)∼r-δ. The dimension d of these networks, as a function of δ, has been studied earlier and has been shown to depend on δ. Here we consider diffusion, annihilation, and chemical reaction processes on these spatially constrained networks and show that their dynamics is controlled by the dimension d of the system. We study, as a function of the exponent δ and the embedding dimension de, the average distance ∼t1/dw a random walker has traveled after t time steps as well as the probability of the random walker's return to the origin P0(t). From these quantities we determine the network dimension d and the dimension dw of the random walk as a function of δ. We find that the fraction d/dw governs the number of survivors as a function of time t in the annihilation process (A+A→0) and in the chemical reaction process (A+B→0), showing that the relations derived for ordered and disordered lattices with short-range links remain valid also in the case of complex embedded networks with long-range links.

Distribution of natural trends in long-term correlated records: a scaling approach.

We estimate the exceedance probability W(x,α;L) that, in a long-term correlated Gaussian-distributed (sub) record of length L characterized by a fluctuation exponent α between 0.5 and 1.5, a relative increase Δ/σ(t) of size larger than x occurs, where Δ is the total observed increase measured by linear regression and σ(t) is the standard deviation around the regression line. We consider L between 500 and 2000, which is the typical length scale of monthly local and reconstructed annual global temperature records. We use scaling theory to obtain an analytical expression for W(x,α;L). From this expression, we can determine analytically, for a given confidence probability Q, the boundaries ±x(Q)(α,L) of the confidence interval. In the presence of an external linear trend, the total observed increase is the sum of the natural and the external increase. An observed relative increase Δ/σ(t) is considered unnatural when it is above x(Q)(α,L). In this case, the size of the external relative increase is bounded by Δ/σ(t)±x(Q)(α,L). We apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends.

Relaxation in ordered systems of ultrafine magnetic particles: effect of the exchange interaction.

We perform Monte Carlo simulations to study the relaxation of single-domain nanoparticles that are located on a simple cubic lattice with anisotropy axes pointing in the z-direction, under the combined influence of anisotropy energy, dipolar interaction and ferromagnetic interaction of strength J. We compare the results of classical Heisenberg systems with three-dimensional magnetic moments [Formula: see text] to those of Ising systems and find that Heisenberg systems show a much richer and more complex dynamical behavior. In contrast to Heisenberg systems, Ising systems need large activation energies to turn a spin and also possess a smaller configuration space for the orientation of the [Formula: see text]. Accordingly, Heisenberg systems possess a whole landscape of different states with very close-lying energies, while Ising systems tend to get frozen in one random state far away from the ground state. For Heisenberg systems, we identify two phase transitions: (i) at intermediate J between domain and layered states and (ii) at larger J between layered and ferromagnetic states. Between these two transitions, the layered states change their appearance and develop a sub-structure, where the orientation of the [Formula: see text] in each layer depends on J, so that for each value of J, a new ground state appears.

Clustering of ventricular arrhythmic complexes in heart rhythm.

We study the statistics of intervals τ between ventricular premature complexes (VPCs) in 24-h electrocardiogram records obtained from PhysioNet data source. We find that the long-term memory inherent in the heartbeat intervals leads to power laws in the probability density function P(τ) between VPCs for τ>6 s. As a consequence, the probability W(t,Δt) that at least one VPC will occur within the next time interval Δt, if the last VPC occurred t time units intervals ago, decays by a power law of t. Based on these results, we suggest a method to obtain a priori information about the occurrence of the next VPC, and how to predict it. We think that usage of this a priori information could be useful for the improvement of the algorithms in healthcare monitoring devices with alarm facilities.

Ion conducting particle networks in liquids: modeling of network percolation and stability.

Networks of inorganic particles (here SiO(2)) formed within organic liquids play an important role in science. Recently they have been considered as 'soggy sand' electrolytes for Li-based batteries with a fascinating combination of mechanical and electrical properties. In this communication we model formation and stability of the networks by Cluster-Cluster Aggregation followed by coarsening on a different time scale. The comparison of computer simulations based on our model with experimental results obtained for LiClO(4) containing polyethylene glycol reveals (i) that the percolation threshold for interfacial conductivity is very small, (ii) that the networks once formed coarsen with a time constant that is roughly independent of volume fraction and size--to a denser aggregate which then stays stable under operating condition. (iii) Trapping of the conducting solvent at high packing is also revealed.