Navigability of temporal networks in hyperbolic space

Navigation on temporal networks

Temporal networks, whose network topology changes over time, are used to represent, e.g., opportunistic mobile networks, vehicle networks, and social contact networks, where two mobile devices (autos or individuals) are connected only when they are close to (interact with) each other. Such networks facilitate the transfer of information. In this paper, we address the problem of navigation on temporal networks: how to route a traffic demand from a source s to a destination d at time t s , based on the network observed before t s ? Whenever the node hosting the information has a contact or interacts with another node, the routing method has to decide whether the information should be forwarded to the contacted node or not. Once the information is forwarded, the contacted node becomes the only node hosting the information. Firstly, we introduce a framework of designing navigation algorithms, in which a distance metric is defined and computed between any node to the target d based on the network observed before t s . Whenever a hosting node has a contact, it forwards the information to the contacted node if the contacted node is closer to the target than the hosting node according to the distance metric. Secondly, we propose systematically distance metrics of a node pair in the temporal network observed, that capture different network properties of a node pair. Thirdly, these metrics or routing strategies are evaluated in empirical contact networks, from the perspective of the time duration of the routing and the probability that the destination can be reached. Their performance is further explained via the correlation between distance metrics and the stability of each metric in ranking nodes' distance to a target node. This work may serve as inspiration for evaluating and redesigning these strategies in other types of networks beyond physical contact networks.

Hyperbolic random geometric graphs: Structural and spectral properties

In this paper we perform a thorough numerical study of structural and spectral properties of hyperbolic random geometric graphs (HRGs) G(n,ρ,α,ζ) by means of a random matrix theory (RMT) approach. HRGs are formed by distributing n nodes in a Poincaré disk of fixed radius ρ; the radial node distribution is characterized by the exponent α and ζ controls the curvature of the embedding space. Specifically, we report and analyze average structural properties [by means of the number of nonisolated vertices V_{x}(G), topological indices, and clustering coefficients] and average spectral properties [by means of standard RMT measures: the ratio between consecutive eigenvalue spacings r_{R}(G), the ratio between nearest- and next-to-nearest-neighbor eigenvalue distances r_{C}(G), and the inverse participation ratio and the Shannon entropy S(G) of the eigenvectors]. Even though HRGs are, in general, more elaborated than Euclidean random geometric graphs, we show that both types of random graphs share important average properties, namely: (i) 〈V_{x}(G)〉 is a simple function of the average degree 〈k〉, 〈V_{x}(G)〉≈n[1-exp(-γ〈k〉)], while (ii) properly normalized 〈r_{R}(G)〉, 〈r_{C}(G)〉 and 〈S(G)〉 scale with the parameter ξ∝〈k〉n^{δ}. Here, γ≡γ(α/ζ), δ≡δ(α/ζ), and 〈·〉 is the average over a graph ensemble.

Optimal navigability of weighted human brain connectomes in physical space

Communication protocols in the brain connectome describe how to transfer information from one region to another. Typically, these protocols hinge on either the spatial distances between brain regions or the intensity of their connections. Yet, none of them combine both factors to achieve optimal efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that integrates link weights and the spatial embedding of connectomes to route signal transmission. We implemented the protocols on connectomes from individuals in two cohorts and on group-representative connectomes designed to capture weighted connectivity properties. We identified an intermediate domain of routing strategies, a sweet spot, where navigation achieves maximum communication efficiency at low transmission cost. This phenomenon is robust and independent of the particular configuration of weights. Our findings suggest an interplay between the intensity of neural connections and their topology and geometry that amplifies communicability, where weights play the role of noise in a stochastic resonance phenomenon. Such enhancement may support more effective responses to external and internal stimuli, underscoring the intricate diversity of brain functions.

Random hyperbolic graphs in d+1 dimensions

We consider random hyperbolic graphs in hyperbolic spaces of any dimension d+1≥2. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to the dimension. Unlike the degree distribution, clustering does depend on the dimension, decreasing to 0 at d→∞. We analyze all of the other limiting regimes of the model, and we release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension.

Deep learning-based methods for natural hazard named entity recognition

Natural hazard named entity recognition is a technique used to recognize natural hazard entities from a large number of texts. The method of natural hazard named entity recognition can facilitate acquisition of natural hazards information and provide reference for natural hazard mitigation. The method of named entity recognition has many challenges, such as fast change, multiple types and various forms of named entities. This can introduce difficulties in research of natural hazard named entity recognition. To address the above problem, this paper constructed a natural disaster annotated corpus for training and evaluation model, and selected and compared several deep learning methods based on word vector features. A deep learning method for natural hazard named entity recognition can automatically mine text features and reduce the dependence on manual rules. This paper compares and analyzes the deep learning models from three aspects: pretraining, feature extraction and decoding. A natural hazard named entity recognition method based on deep learning is proposed, namely XLNet-BiLSTM-CRF model. Finally, the research hotspots of natural hazards papers in the past 10 years were obtained through this model. After training, the precision of the XLNet-BilSTM-CRF model is 92.80%, the recall rate is 91.74%, and the F1-score is 92.27%. The results show that this method, which is superior to other methods, can effectively recognize natural hazard named entities.

Dynamic hidden-variable network models

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The dynamics is controlled by two parameters: one that tunes the rate of change of hidden variables and another that tunes the rate at which node pairs reevaluate their connections given the current values of hidden variables. Snapshots of networks in the dynamic models are equivalent to networks generated by the static models only if the link reevaluation rate is sufficiently larger than the rate of hidden-variable dynamics or if an additional mechanism is added whereby links actively respond to changes in hidden variables. Otherwise, links are out of equilibrium with respect to hidden variables and network snapshots exhibit structural deviations from the static models. We examine the level of structural persistence in the considered models and quantify deviations from staticlike behavior. We explore temporal versions of popular static models with community structure, latent geometry, and degree heterogeneity. While we do not attempt to directly model real networks, we comment on interesting qualitative resemblances to real systems. In particular, we speculate that links in some real networks are out of equilibrium with respect to hidden variables, partially explaining the presence of long-ranged links in geometrically embedded systems and intergroup connectivity in modular systems. We also discuss possible extensions, generalizations, and applications of the introduced class of dynamic network models.

Hyperbolic mapping of human proximity networks

Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases and information among humans. Here we address the problem of mapping human proximity networks into hyperbolic spaces. Each snapshot of these networks is often very sparse, consisting of a small number of interacting (i.e., non-zero degree) nodes. Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using methods developed for traditional (non-mobile) complex networks. We justify this compatibility theoretically and validate it experimentally. We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision. Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems.

Link persistence and conditional distances in multiplex networks

Recent progress towards unraveling the hidden geometric organization of real multiplexes revealed significant correlations across the hyperbolic node coordinates in different network layers, which facilitated applications like translayer link prediction and mutual navigation. But, are geometric correlations alone sufficient to explain the topological relation between the layers of real systems? Here, we provide the negative answer to this question. We show that connections in real systems tend to persist from one layer to another irrespective of their hyperbolic distances. This suggests that in addition to purely geometric aspects, the explicit link formation process in one layer impacts the topology of other layers. Based on this finding, we present a simple modification to the recently developed geometric multiplex model to account for this effect, and show that the extended model can reproduce the behavior observed in real systems. We also find that link persistence is significant in all considered multiplexes and can explain their layers' high edge overlap, which cannot be explained by coordinate correlations alone. Furthermore, by taking both link persistence and hyperbolic distance correlations into account, we can improve translayer link prediction. These findings guide the development of multiplex embedding methods, suggesting that such methods should account for both coordinate correlations and link persistence across layers.

Geometric characterisation of disease modules

There is an increasing accumulation of evidence supporting the existence of a hyperbolic geometry underlying the network representation of complex systems. In particular, it has been shown that the latent geometry of the human protein network (hPIN) captures biologically relevant information, leading to a meaningful visual representation of protein-protein interactions and translating challenging systems biology problems into measuring distances between proteins. Moreover, proteins can efficiently communicate with each other, without global knowledge of the hPIN structure, via a greedy routing (GR) process in which hyperbolic distances guide biological signals from source to target proteins. It is thanks to this effective information routing throughout the hPIN that the cell operates, communicates with other cells and reacts to environmental changes. As a result, the malfunction of one or a few members of this intricate system can disturb its dynamics and derive in disease phenotypes. In fact, it is known that the proteins associated with a single disease agglomerate non-randomly in the same region of the hPIN, forming one or several connected components known as the disease module (DM). Here, we present a geometric characterisation of DMs. First, we found that DM positions on the two-dimensional hyperbolic plane reflect their fragmentation and functional heterogeneity, rendering an informative picture of the cellular processes that the disease is affecting. Second, we used a distance-based dissimilarity measure to cluster DMs with shared clinical features. Finally, we took advantage of the GR strategy to study how defective proteins affect the transduction of signals throughout the hPIN.