اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLatent geometry and dynamics of proximity networks
112
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena and the performance of routing algorithms. Yet, the mechanisms responsible for their observed characteristics remain elusive. Here, we show that many of the observed properties of proximity networks emerge naturally and simultaneously in a simple latent space network model, called dynamic-$mathbb{S}^{1}$. The dynamic-$mathbb{S}^{1}$ does not model node mobility directly, but captures the connectivity in each snapshot---each snapshot in the model is a realization of the $mathbb{S}^{1}$ model of traditional complex networks, which is isomorphic to hyperbolic geometric graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, inter-contact and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Interestingly, we find that network temperature plays a central role in network dynamics, dictating the exponents of these distributions, the time-aggregated agent degrees, and the formation of unique and recurrent components. Further, we show that paradigmatic epidemic and rumor spreading processes perform similarly in real and modeled networks. The dynamic-$mathbb{S}^{1}$ or extensions of it may apply to other types of time-varying networks and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems.
قيم البحث
اقرأ أيضاً
Networks of interdisciplinary teams, biological interactions as well as food webs are examples of networks that are shaped by complementarity principles: connections in these networks are preferentially established between nodes with complementary pr
operties. We propose a geometric framework for complementarity-driven networks. In doing so we first argue that traditional geometric representations, e.g., embeddings of networks into latent metric spaces, are not applicable to complementarity-driven networks due to the contradiction between the triangle inequality in latent metric spaces and the non-transitivity of complementarity. We then propose the cross-geometric representation for these complementarity-driven networks and demonstrate that this representation (i) follows naturally from the complementarity rule, (ii) is consistent with the metric property of the latent space, (iii) reproduces structural properties of real complementarity-driven networks, if the latent space is the hyperbolic disk, and (iv) allows for prediction of missing links in complementarity-driven networks with accuracy surpassing existing similarity-based methods. The proposed framework challenges social network analysis intuition and tools that are routinely applied to complementarity-driven networks and offers new avenues towards descriptive and prescriptive analysis of systems in science of science and biomedicine.
We propose a network metric, edge proximity, ${cal P}_e$, which demonstrates the importance of specific edges in a network, hitherto not captured by existing network metrics. The effects of removing edges with high ${cal P}_e$ might initially seem in
conspicuous but are eventually shown to be very harmful for networks. Compared to existing strategies, the removal of edges by ${cal P}_e$ leads to a remarkable increase in the diameter and average shortest path length in undirected real and random networks till the first disconnection and well beyond. ${cal P}_e$ can be consistently used to rupture the network into two nearly equal parts, thus presenting a very potent strategy to greatly harm a network. Targeting by ${cal P}_e$ causes notable efficiency loss in U.S. and European power grid networks. ${cal P}_e$ identifies proteins with essential cellular functions in protein-protein interaction networks. It pinpoints regulatory neural connections and important portions of the neural and brain networks, respectively. Energy flow interactions identified by ${cal P}_e$ form the backbone of long food web chains. Finally, we scrutinize the potential of ${cal P}_e$ in edge controllability dynamics of directed networks.
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-w
orld, Barabasi-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.
Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the pro
jection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks, and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model, and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Social network based information campaigns can be used for promoting beneficial health behaviours and mitigating polarisation (e.g. regarding climate change or vaccines). Network-based intervention strategies typically rely on full knowledge of netwo
rk structure. It is largely not possible or desirable to obtain population-level social network data due to availability and privacy issues. It is easier to obtain information about individuals attributes (e.g. age, income), which are jointly informative of an individuals opinions and their social network position. We investigate strategies for influencing the system state in a statistical mechanics based model of opinion formation. Using synthetic and data based examples we illustrate the advantages of implementing coarse-grained influence strategies on Ising models with modular structure in the presence of external fields. Our work provides a scalable methodology for influencing Ising systems on large graphs and the first exploration of the Ising influence problem in the presence of ambient (social) fields. By exploiting the observation that strong ambient fields can simplify control of networked dynamics, our findings open the possibility of efficiently computing and implementing public information campaigns using insights from social network theory without costly or invasive levels of data collection.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
