Measuring the dimension of partially embedded networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network's large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(r) ~ 1/r. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures

Discovering New Sentiments from the Social Web

A persistent challenge in Complex Systems (CS) research is the phenomenological reconstruction of systems from raw data. In order to face the problem, the use of sound features to reason on the system from data processing is a key step. In the specific case of complex societal systems, sentiment analysis allows to mirror (part of) the affective dimension. However it is not reasonable to think that individual sentiment categorization can encompass the new affective phenomena in digital social networks. The present papers addresses the problem of isolating sentiment concepts which emerge in social networks. In an analogy to Artificial Intelligent Singularity, we propose the study and analysis of these new complex sentiment structures and how they are similar to or diverge from classic conceptual structures associated to sentiment lexicons. The conjecture is that it is highly probable that hypercomplex sentiment structures -not explained with human categorizations- emerge from high dynamic social information networks. Roughly speaking, new sentiment can emerge from the new global nervous systems as it occurs in humans

Correlation Dimension of Complex Networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers

Correlation dimension of complex networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers

Gossip-Based Indexing Ring Topology for 2-Dimension Spatial Data in Overlay Networks

AbstractOverlay networks are used widely in the Internet, such as retrieval and share of files, multimedia games and so on. However, in distributed system, the retrieval and share of 2-dimension spatial data still have some difficult problems and can not solve the complex retrieval of 2-dimension spatial data efficiently. This article presents a new indexing overlay networks, named 2D-Ring, which is the ring topology based on gossip for 2-dimension spatial data. The peers in our overlay networks exchange the information periodically and update each local view by constructing algorithm. 2-dimension spatial data is divided by quad-tree and mapped into control points, which are hashed into 2D-Ring by SHA-1 hash function. In such way, the problem of 2-dimension spatial data indexing is converted to the problem of searching peers in the 2D-Ring. A large of extensive experiments show that the time complexity of constructing algorithm of 2D-Ring can reach convergence logarithmically as a function of the network size and hold higher hit rate and lower query delay

Overview 2010 of ARL Program on Network Science for Human Decision Making

The Army Research Laboratory program on the Network Science of Human Decision Making brings together researchers from a variety of disciplines to work on a complex research problem that defies confinement within any single discipline. Consequently, new and rewarding solutions have been obtained for a problem of importance to society and the Army, that being, the human dimension of complex networks. This program investigates the basic research foundation of a science of networks supporting the linkage between the cognitive and social domains as they relate to human decision making. The research strategy extends recent methods of non-equilibrium statistical physics to non-stationary, renewal stochastic processes characteristic of the interactions among nodes in complex networks. The theoretical analyses of complex networks, although mathematically rigorous, often elude analytic solutions and require simulation and computation to analyze the underlying dynamic process. The information transfer between two complex networks is calculated using the principle of complexity management as well as direct numerical calculation of the decision making model developed within the project

BL-MNE: Emerging Heterogeneous Social Network Embedding through Broad Learning with Aligned Autoencoder

Network embedding aims at projecting the network data into a low-dimensional feature space, where the nodes are represented as a unique feature vector and network structure can be effectively preserved. In recent years, more and more online application service sites can be represented as massive and complex networks, which are extremely challenging for traditional machine learning algorithms to deal with. Effective embedding of the complex network data into low-dimension feature representation can both save data storage space and enable traditional machine learning algorithms applicable to handle the network data. Network embedding performance will degrade greatly if the networks are of a sparse structure, like the emerging networks with few connections. In this paper, we propose to learn the embedding representation for a target emerging network based on the broad learning setting, where the emerging network is aligned with other external mature networks at the same time. To solve the problem, a new embedding framework, namely "Deep alIgned autoencoder based eMbEdding" (DIME), is introduced in this paper. DIME handles the diverse link and attribute in a unified analytic based on broad learning, and introduces the multiple aligned attributed heterogeneous social network concept to model the network structure. A set of meta paths are introduced in the paper, which define various kinds of connections among users via the heterogeneous link and attribute information. The closeness among users in the networks are defined as the meta proximity scores, which will be fed into DIME to learn the embedding vectors of users in the emerging network. Extensive experiments have been done on real-world aligned social networks, which have demonstrated the effectiveness of DIME in learning the emerging network embedding vectors.Comment: 10 pages, 9 figures, 4 tables. Full paper is accepted by ICDM 2017, In: Proceedings of the 2017 IEEE International Conference on Data Mining

A "Social Bitcoin" could sustain a democratic digital world

A multidimensional financial system could provide benefits for individuals, companies, and states. Instead of top-down control, which is destined to eventually fail in a hyperconnected world, a bottom-up creation of value can unleash creative potential and drive innovations. Multiple currency dimensions can represent different externalities and thus enable the design of incentives and feedback mechanisms that foster the ability of complex dynamical systems to self-organize and lead to a more resilient society and sustainable economy. Modern information and communication technologies play a crucial role in this process, as Web 2.0 and online social networks promote cooperation and collaboration on unprecedented scales. Within this contribution, we discuss how one dimension of a multidimensional currency system could represent socio-digital capital (Social Bitcoins) that can be generated in a bottom-up way by individuals who perform search and navigation tasks in a future version of the digital world. The incentive to mine Social Bitcoins could sustain digital diversity, which mitigates the risk of totalitarian control by powerful monopolies of information and can create new business opportunities needed in times where a large fraction of current jobs is estimated to disappear due to computerisation.Comment: Contribution to EPJ-ST special issue on 'Can economics be a Physical Science?', edited by S. Sinha, A. S. Chakrabarti & M. Mitr