Session A56: Network Theory I

Geometric renormalization of complex networks

Complex networks are small-world, strongly clustered and hierarchical, modular, robust yet fragile, and may exhibit unexpected responses like cascades and other critical and extreme events. Many of these fundamental properties are well explained by a family of hidden metric space network models that led to the discovery that the latent geometry of many real networks is hyperbolic. Hyperbolicity emerges as a result of the combination of popularity and similarity dimensions into an effective distance between nodes, such that more popular and similar nodes have more chance to interact. The geometric approach permits the production of truly cartographic maps of real networks that are not only visually appealing, but enable applications like efficient navigation and the detection of communities of similar nodes. Recently, it has also enabled the introduction of a geometric renormalization group that unravels the multiple length scales coexisting in complex networks, strongly intertwined due to their small world property. Interestingly, many real-world networks are self-similar when observed at the different resolutions unfolded by geometric renormalization, a property that may find its origin in a common growth mechanism. Practical applications of the geometric renormalization group for networks include high-fidelity downscaled or upscaled network replicas, and many others.   

Model-dependent and model-independent control of biological network models

Network models of cell signaling and regulation are ubiquitous because of their ability to integrate the current knowledge of a biological process and test new findings and hypotheses. An often asked question is how to control a network model and drive it towards its dynamical attractors (which are often identifiable with phenotypes or stable patterns of activity of the modeled system), and which nodes and interventions are required to do so. In this talk, we introduce two recently developed network control methods - feedback vertex set control and stable motif control - that use the graph structure of a network model to identify nodes that drive the system towards an attractor of interest (i.e., nodes sufficient for attractor control). Feedback vertex set control makes predictions that apply to all network models with a given graph structure and stable motif control makes predictions for a specific model instance, and this allows us to compare the results of model-independent and model-dependent network control. We illustrate these methods with various examples and discuss the aspects of each method that makes its predictions dependent or independent of the model.   

Discovering the genes mediating the interactions between chronic respiratory diseases in the human interactome

Biological networks are powerful resources for the discovery of potential candidate genes and for the investigation of the mechanisms underlying human complex disease like asthma and chronic obstructive pulmonary disease (COPD). Recent network-based computational studies have shown that disease genes encoding proteins have a strong tendency to interact with each other and to agglomerate in specific 'disease modules' identified as connected localized neighborhoods in the network [1]. In this scenario, perturbations originating within one disease module can diffuse through the network and affect other close diseases [2].
Recognizing the genes mediating such perturbations is crucial for understanding the biological pathways responsible for the comorbidity of similar diseases such as asthma and COPD. In this work, we identify the topological modules of these two diseases in the protein-protein interaction network and determine their mediators by defining a variant of betweenness centrality measure, called 'flow centrality'. The biological role of the observed flow central genes sheds light on the hypothesized common genetic origin of asthma and COPD [3].

[1] Barabasi et al., Nature Reviews Genetics (2011)
[2] Menche et al., Science (2015)
[3] Postma et al., JACI (2015)   

The New Field of Network Physiology: Mapping the Human Physiolome

The human organism is an integrated network where complex physiological systems continuously interact to optimize and coordinate their function. Organ-to-organ interactions occur at multiple levels and spatiotemporal scales to produce distinct physiologic states. Disrupting organ communications can lead to dysfunction of individual systems or to collapse of the entire organism. Yet, we do not know the nature of interactions among systems and sub-systems, and their collective role as a network in maintaining health. The new field of Network Physiology aims to address these fundamental questions.

Through the prism of concepts and approaches from statistical and computational physics and nonlinear dynamics, we will present a new framework to identify and quantify dynamic networks of organ interactions. We will demonstrate how physiologic network topology and systems connectivity lead to integrated global behaviors representative of distinct states and functions.

The presented investigations are initial steps in building a first Atlas of dynamic interactions among organ systems and the Human Physiolome, a new kind of BigData of blue-print reference maps that uniquely represent physiologic states and functions under health and disease.   

Complex statistical interactions in biology

Although each individual carries dozens of deleterious mutations, each of which should have a dramatic impact on our health, life carries on due to extensive genetic buffering. Therefore, interpreting genetic information requires the understanding of not only the impact of individual mutations but also their interactions. Genetic interactions occur when the combined impact of two mutations results in an unexpected phenotype, for example a positive interaction in the case of genetic buffering. Negative interactions are even more striking, such as synthetic lethality, where two individually mild mutations lead to cell death. Understanding and predicting (even higher order) genetic interactions is a key to better understand complex traits, missing heritability and genetic buffering in humans. In the talk we will overview the major sources of data and recently developed statistical methods to analyze and predict it. Our results enable us to better understand the emergence of biological function under both healthy and pathological conditions and directly contribute to improved disease module identification, drug target prediction, and drug combination design.   

Reconstructing model humans from observed health data

Human aging can be understood as a stochastic process of damage accumulation. This stochasticity is evident in the heterogeneity of health trajectories and lifespans of individuals. Measurements of health “deficits” can be used to quantify an individual's state of health. We model human aging using a network of interacting health deficits with stochastic damage/repair. Our model incorporates both “observed” nodes, corresponding to observed deficits, and “hidden” nodes, representing the large amount of health aspects that are not measured. We use maximum likelihood techniques to estimate parameters with observed human data of deficits and death ages. We then generate individuals from our model using these estimated parameters, so that they have health trajectories distributed approximately the same as the data. This lets us extrapolate from observed data to future health trajectories and lifespans.   

Emergence of Laplace-Distributed Growth Rates in Network Dynamics

The dynamical state of a complex network is rarely stationary in time, often exhibiting sufficiently erratic fluctuations so as to seem random. Previous observational studies on annual fish catches, flock sizes of migrating birds, and company sales have revealed that the growth rates follow a Laplace (double exponential) distribution, which is characterized by a higher probability of large increases/decreases relative to the Gaussian growth statistics predicted by typical null models. Yet despite the prevalence of Laplacian growth rates in disparate systems, their mechanistic origin has remained elusive. Here we show that Laplacian growth statistics emerge generically from the interplay between two ubiquitous features in real complex systems — multistability and noise. Under specific conditions, these factors combine to allow frequent transitions between the underlying attraction basins, which broadens tails of the growth distribution relative to that produced by a random walk. Our results suggests that “boom and bust” behavior may be the rule rather than the exception in networks with nonlinear dynamics, with implications for problems ranging from sustainable ecosystem management to financial system stability.   

Spreading dynamics of forget-remember mechanism

We study extensively the forget-remember mechanism (FRM) for message spreading, originally introduced in [Eur. Phys. J. B 62, 247 (2008)]. The freedom of specifying forget-remember functions governing the FRM can enrich the spreading dynamics to a very large extent. The master equation is derived for describing the FRM dynamics. By applying the mean field techniques, we have shown how the steady states can be reached under certain conditions, which agrees well with the Monte Carlo simulations. The distributions of forget and remember times can be explicitly given when the forget-remember functions take linear or exponential forms, which might shed some light on understanding the temporal nature of diseases like flu. For time-dependent FRM there is an epidemic threshold related to the FRM parameters. We have proven that the mean field critical transmissibility for the SIS model and the critical transmissibility for the SIR model are the lower and the the upper bounds of the critical transmissibility for the FRM model, respectively.   

Measuring and Modeling the Flow of Information Online and on Networks

We propose a model for the flow of information in the form of symbolic data. Nodes in a graph representing, e.g., a social network take turns generating words, leading to a symbolic time series associated with each node. Information propagates over the graph via a quoting mechanism, where nodes randomly copy short symbolic sequences from each other. We characterize information flows from these data via information-theoretic estimators, and we derive analytic relationships between model parameters and the values of these estimators. We explore and validate the model with simulations on small network motifs and larger random graphs. Tractable models such as ours that generate symbolic data while controlling the information flow allow us to test and compare measures of information flow applicable to realistic data. In particular, by choosing different network structures, we can develop test scenarios to determine whether or not measures of information flow can distinguish between true and spurious interactions, and how topological network properties relate to information flow.   

Scale-free Networks Well Done

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real networks. We first provide rigorous definitions of scale-free and power-law distributions, the latter equivalent to the definition of regularly varying distributions in statistics. These definitions allow the distribution to deviate from a pure power law arbitrarily but without affecting the power-law tail exponent. We then identify three estimators of these exponents that are proven to be statistically consistent - that is, converging to the true exponent value for any regularly varying distribution - and that satisfy some additional niceness requirements. Finally, we apply these estimators to a representative collection of synthetic and real data to find that real scale-free networks are definitely not as rare as one would conclude based on the popular but unrealistic assumption that real data comes from power laws of pristine purity, void of noise and deviations.   

Network architecture of energy landscapes in mesoscopic quantum systems

Mesoscopic quantum systems exhibit complex many-body phenomena. Even simple, non-interacting theories display a rich landscape of energy states, where many-particle configurations are linked by spin- and energy-dependent transition rates. This collective energy landscape is difficult to characterize, especially in regimes of frustration. Here, we use network science to quantify the organization of these state transitions. Using a computational model of electronic transport through quantum antidots, we construct networks where nodes represent energy states and edges represent allowed transitions. We explore how current and conductance, which measure transport, are reflected in the network topology in response to changes in external voltages. We find that the state-transition networks exhibit Rentian scaling, which is characteristic of efficient computer and neural circuitry, and which measures the interconnection complexity of a network. Remarkably, networks corresponding to points of frustration in transport exhibit enhanced complexity relative to networks not experiencing frustration. Our results demonstrate that network-based analyses can capture salient properties of quantum transport, and motivate future efforts using network science to understand complex quantum systems.