Amir Bashan

Network physiology reveals relations between network topology and physiological function

The human organism is an integrated network where complex physiological systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here we develop a framework to probe interactions among diverse systems, and we identify a physiological network. We find that each physiological state is characterized by a specific network structure, demonstrating a robust interplay between network topology and function. Across physiological states, the network undergoes topological transitions associated with fast reorganization of physiological interactions on time scales of a few minutes, indicating high network flexibility in response to perturbations. The proposed system-wide integrative approach may facilitate the development of a new field, Network Physiology.

Comparison of detrending methods for fluctuation analysis

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA performs the same as DFA in long data with weak trends and is slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.

The extreme vulnerability of interdependent spatially embedded networks

Networks of networks are vulnerable: a failure in one sub-network can bring the rest crashing down. Previous simulations have suggested that randomly positioned networks might offer some limited robustness under certain circumstances. Analysis now shows, however, that real-world interdependent networks, where nodes are positioned according to geographical constraints, might not be so resilient.

Universality of human microbial dynamics

The recent realization that human-associated microbial communities play a crucial role in determining our health and well-being1,2 has led to the ongoing development of microbiome-based therapies3 such as fecal microbiota transplantation4,5. Thosemicrobial communities are very complex, dynamic6 and highly personalized ecosystems3,7, exhibiting a high degree of inter-individual variability in both species assemblages8 and abundance profiles9. It is not known whether the underlying ecological dynamics, which can be parameterized by growth rates, intra- and inter-species interactions in population dynamics models10, are largely host-independent (i.e. “universal”) or host-specific. If the inter-individual variability reflects host-specific dynamics due to differences in host lifestyle11, physiology12, or genetics13, then generic microbiome manipulations may have unintended consequences, rendering them ineffectual or even detrimental. Alternatively, microbial ecosystems of different subjects may follow a universal dynamics with the inter-individual variability mainly stemming from differences in the sets of colonizing species7,14. Here we developed a novel computational method to characterize human microbial dynamics. Applying this method to cross-sectional data from two large-scale metagenomic studies, the Human Microbiome Project9,15 and the Student Microbiome Project16, we found that both gut and mouth microbiomes display pronounced universal dynamics, whereas communities associated with certain skin sites are likely shaped by differences in the host environment. Interestingly, the universality of gut microbial dynamics is not observed in subjects with recurrent Clostridium difficile infection17 but is observed in the same set of subjects after fecal microbiota transplantation. These results fundamentally improve our understanding of forces and processes shaping human microbial ecosystems, paving the way to design general microbiome-based therapies18.

Percolation in networks composed of connectivity and dependency links

Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second-order transition found in classical networks. We analytically analyze the effect of different distributions of dependencies links on the robustness of networks. For a random Erdös-Rényi (ER) network with average degree k that is divided into dependency clusters of size s, the fraction of nodes that belong to the giant component P(∞) is given by P(∞)=p(s-1)[1-exp(-kpP(∞))](s), where 1-p is the initial fraction of removed nodes. Our general result coincides with the known Erdös-Rényi equation for random networks for s=1. For networks with Poissonian distribution of dependency links we find that P(∞) is given by P(∞)=f(k,p)(P(∞))e(([s]-1)[pf(k,p)(P(∞))-1]), where f(k,p)(P(∞))≡1-exp(-kpP(∞)) and [s] is the mean value of the size of dependency clusters. For networks with Gaussian distribution of dependency links we show how the average and width of the distribution affect the robustness of the networks.

Localized attacks on spatially embedded networks with dependencies

Many real world complex systems such as critical infrastructure networks are embedded in space and their components may depend on one another to function. They are also susceptible to geographically localized damage caused by malicious attacks or natural disasters. Here, we study a general model of spatially embedded networks with dependencies under localized attacks. We develop a theoretical and numerical approach to describe and predict the effects of localized attacks on spatially embedded systems with dependencies. Surprisingly, we find that a localized attack can cause substantially more damage than an equivalent random attack. Furthermore, we find that for a broad range of parameters, systems which appear stable are in fact metastable. Though robust to random failures—even of finite fraction—if subjected to a localized attack larger than a critical size which is independent of the system size (i.e., a zero fraction), a cascading failure emerges which leads to complete system collapse. Our results demonstrate the potential high risk of localized attacks on spatially embedded network systems with dependencies and may be useful for designing more resilient systems.Many real world complex systems such as infrastructure, communication and transportation networks are embedded in space, where entities of one system may depend on entities of other systems. These systems are subject to geographically localized failures due to malicious attacks or natural disasters. Here we study the resilience of a system composed of two interdependent spatially embedded networks to localized geographical attacks. We find that if an attack is larger than a finite (zero fraction of the system) critical size, it will spread through the entire system and lead to its complete collapse. If the attack is below the critical size, it will remain localized. In contrast, under random attack a finite fraction of the system needs to be removed to initiate system collapse. We present both numerical simulations and a theoretical approach to analyze and predict the effect of local attacks and the critical attack size. Our results demonstrate the high risk of local attacks on interdependent spatially embedded infrastructures and can be useful for designing more resilient systems.

Network Physiology: How Organ Systems Dynamically Interact.

We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems.

Percolation and cascade dynamics of spatial networks with partial dependency

Recently, it has been shown that the removal of a random fraction of nodes from a system of interdependent spatial networks can lead to cascading failures which amplify the original damage and destroy the entire system, often via abrupt first-order transitions. For these distinctive phenomena to emerge, the interdependence between networks need not be total. We consider here a system of partially interdependent spatial networks (modelled as lattices) with a fraction q of the nodes interdependent and the remaining 1 − q autonomous. In our model, the dependency links between networks are of geometric length less than r. Under full dependency (q = 1), this system was shown to have a first-order percolation transition if r > rc ≈ 8. Here, we generalize this result and show that for all q > 0, there will be a first-order transition if r > rc(q). We show that rc(q) increases monotonically with decreasing q and limq→0+ rc(q) = ∞. Additionally, we present a detailed description and explanation of the cascading failures in spatially embedded interdependent networks near the percolation threshold pc. These failures follow three mechanisms depending on the value of r. Below rc the system undergoes a continuous transition similar to standard percolation on a lattice. Above rc there are two distinct first-order transitions for finite and infinite r, respectively. The cascading failure for finite r is characterized by the emergence of a critical hole which then spreads through the system while the infinite r transition is more similar to the case of random networks. Surprisingly, we find that this spreading transition can still occur even if p < pc. We present measurements of cascade dynamics which differentiate between these phase transitions and elucidate their mechanisms. These results extend previous research on spatial networks to the more realistic case of partial dependency and shed new light on the specific dynamics of dependencydriven cascading failures.

An Introduction to Interdependent Networks

Many real-world phenomena can be modelled using networks. Often, these networks interact with one another in non-trivial ways. Recently, a theory of interdependent networks has been developed which describes dependency between nodes across networks. Interdependent networks have a number of unique properties which are absent in single networks. In particular, systems of interdependent networks often undergo abrupt first-order percolation transitions induced by cascading failures. Here we present an overview of recent developments and significant findings regarding interdependent networks and networks of networks.

On the Origins and Control of Community Types in the Human Microbiome

Microbiome-based stratification of healthy individuals into compositional categories, referred to as “enterotypes” or “community types”, holds promise for drastically improving personalized medicine. Despite this potential, the existence of community types and the degree of their distinctness have been highly debated. Here we adopted a dynamic systems approach and found that heterogeneity in the interspecific interactions or the presence of strongly interacting species is sufficient to explain community types, independent of the topology of the underlying ecological network. By controlling the presence or absence of these strongly interacting species we can steer the microbial ecosystem to any desired community type. This open-loop control strategy still holds even when the community types are not distinct but appear as dense regions within a continuous gradient. This finding can be used to develop viable therapeutic strategies for shifting the microbial composition to a healthy configuration.