Abstract-The

High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks 1-3 . Specifically, we demonstrate that we can find functional modules 4,5 in complex networks, and classify nodes into universal roles according to their pattern of intra-and inter-module connections. The method thus yields a 'cartographic representation' of complex networks. Metabolic networks 6-8 are among the most challenging biological networks and, arguably, the ones with most potential for immediate applicability 9 . We use our method to analyse the metabolic networks of twelve organisms from three different superkingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that metabolites that participate in only a few reactions but that connect different modules are more conserved than hubs whose links are mostly within a single module.If we are to extract the significant information from the topology of a large, complex network, knowledge of the role of each node is of crucial importance. A cartographic analogy is helpful to illustrate this point. Consider the network formed by all cities and towns in a country (the nodes) and all the roads that connect them (the links). It is clear that a map in which each city and town is represented by a circle of fixed size and each road is represented by a line of fixed width is hardly useful. Rather, real maps emphasize capitals and important communication lines so that we can obtain scale-specific information at a glance. Similarly, it is difficult, if not impossible, to obtain information from a network with hundreds or thousands of nodes and links, unless the information about nodes and links is conveniently summarized. This is particularly true for biological networks.Here, we propose a methodology, which is based on the connectivity of the nodes, that yields a cartographic representation of a complex network. The first step in our method is to identify the functional modules 4,5 in the network. In the cartographic picture, modules are analogous to countries or regions, and enable a coarse-grained, and thus simplified, description of the network. Then we classify the nodes in the network into a small number of system-independent 'universal roles'.It is common that social networks have communities of highly interconnected nodes that are less connected to nodes in other communities. Such modular structures have been reported not only in social networks 5,10-12 , but also in food webs 13 and biochemical networks 4,14-16 . It is widely believed that the modular structure of complex networks plays a critical role in

We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era.A hallmark of physiologic systems is their extraordinary complexity. The nonstationarity and nonlinearity of signals ( Fig. 1) generated by living organisms defy traditional mechanistic approaches based on homeostasis and conventional biostatistical methodologies. Recognition that physiologic time series contain ''hidden information'' has fueled growing interest in applying concepts and techniques from statistical physics, including chaos theory, to a wide range of biomedical problems from molecular to organismic levels (1, 2).This presentation describes one area of investigation that has engaged our collaborative attention, namely, fractal analysis of physiologic time series in health and disease. The discussion will focus primarily on certain features of the human heartbeat, one important example of complex physiologic fluctuations. The dynamics of another physiologic control system-human gait-is also briefly discussed. Recognizing that this topic represents only one selected aspect of the broad and rapidly expanding applications of complexity theory to biomedicine (Table 1), readers are referred to a number of useful reviews and references therein (1, 3-10).A motivating problem for our work is depicted in Fig. 1, which presents a dynamical self-test. Shown are 30-min heart rate time series from four subjects. Only one is from a healthy individual; the other three are from patients with life-threatening forms of heart disease. The problem is to identify the normal record. The (perhaps nonintuitive) answer to this ''test'' is given in the figure caption. Beyond its obvious diagnostic import, the problem of classifying temporal assays of integrated cardiac physiology has implications for understanding a...

We analyze the global structure of the worldwide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the worldwide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multicommunity structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints and that geopolitical considerations have to be taken into account. We identify each city's global role based on its pattern of intercommunity and intracommunity connections, which enables us to obtain scale-specific representations of the network.complex networks ͉ betweenness centrality ͉ critical infrastructures

Rationale: The contributions of diverse cell populations in the human lung to pulmonary fibrosis pathogenesis are poorly understood. Single-cell RNA sequencing can reveal changes within individual cell populations during pulmonary fibrosis that are important for disease pathogenesis. Objectives: To determine whether single-cell RNA sequencing can reveal disease-related heterogeneity within alveolar macrophages, epithelial cells, or other cell types in lung tissue from subjects with pulmonary fibrosis compared with control subjects. Methods: We performed single-cell RNA sequencing on lung tissue obtained from eight transplant donors and eight recipients with pulmonary fibrosis and on one bronchoscopic cryobiospy sample from a patient with idiopathic pulmonary fibrosis. We validated these data using in situ RNA hybridization, immunohistochemistry, and bulk RNA-sequencing on flow-sorted cells from 22 additional subjects. Measurements and Main Results: We identified a distinct, novel population of profibrotic alveolar macrophages exclusively in patients with fibrosis. Within epithelial cells, the expression of genes involved in Wnt secretion and response was restricted to nonoverlapping cells. We identified rare cell populations including airway stem cells and senescent cells emerging during pulmonary fibrosis. We developed a web-based tool to explore these data. Conclusions: We generated a single-cell atlas of pulmonary fibrosis. Using this atlas, we demonstrated heterogeneity within alveolar macrophages and epithelial cells from subjects with pulmonary fibrosis. These results support the feasibility of discovery-based approaches using next-generation sequencing technologies to identify signaling pathways for targeting in the development of personalized therapies for patients with pulmonary fibrosis.

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues lambda(i) of C against a "null hypothesis"--a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [lambda(-),lambda(+)] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these "deviating eigenvectors" are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.