Communicability across evolving networks

Many natural and technological applications generate time ordered sequences of networks, defined over a fixed set of nodes; for example time-stamped information about ‘who phoned who’ or ‘who came into contact with who’ arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the non-mutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction.

Stratospheric temperature trends: our evolving understanding

We review the scientific literature since the 1960s to examine the evolution of modeling tools and observations that have advanced understanding of global stratospheric temperature changes. Observations show overall cooling of the stratosphere during the period for which they are available (since the late 1950s and late 1970s from radiosondes and satellites, respectively), interrupted by episodes of warming associated with volcanic eruptions, and superimposed on variations associated with the solar cycle. There has been little global mean temperature change since about 1995. The temporal and vertical structure of these variations are reasonably well explained bymodels that include changes in greenhouse gases, ozone, volcanic aerosols, and solar output, although there are significant uncertainties in the temperature observations and regarding the nature and influence of past changes in stratospheric water vapor. As a companion to a recent WIREs review of tropospheric temperature trends, this article identifies areas of commonality and contrast between the tropospheric and stratospheric trend literature. For example, the increased attention over time to radiosonde and satellite data quality has contributed to better characterization of uncertainty in observed trends both in the troposphere and in the lower stratosphere, and has highlighted the relative deficiency of attention to observations in the middle and upper stratosphere. In contrast to the relatively unchanging expectations of surface and tropospheric warming primarily induced by greenhouse gas increases, stratospheric temperature change expectations have arisen from experiments with a wider variety of model types, showingmore complex trend patterns associated with a greater diversity of forcing agents.

Multiscale evolving complex network model of functional connectivity in neuronal cultures

Cultures of cortical neurons grown on multielectrode arrays exhibit spontaneous, robust and recurrent patterns of highly synchronous activity called bursts. These bursts play a crucial role in the development and topological selforganization of neuronal networks. Thus, understanding the evolution of synchrony within these bursts could give insight into network growth and the functional processes involved in learning and memory. Functional connectivity networks can be constructed by observing patterns of synchrony that evolve during bursts. To capture this evolution, a modelling approach is adopted using a framework of emergent evolving complex networks and, through taking advantage of the multiple time scales of the system, aims to show the importance of sequential and ordered synchronization in network function.

The functional neuroanatomy of the evolving parent-infant relationship

Infant survival and the development of secure and cooperative relationships are central to the future of the species. In humans, this relies heavily on the evolving early parent–infant social and affective relationship. While much is known about the behavioural and psychological components of this relationship, relatively little is known about the underlying functional neuroanatomy. Affective and social neuroscience has helped to describe the main adult brain networks involved, but has so far engaged very little with developmental findings. In this review, we seek to highlight future avenues for research by providing a coherent framework for describing the parent–infant relationship over the first 18 months. We provide an outline of the evolving nature of the relationship, starting with basic orienting and recognition processes, and culminating in the infant's attainment of higher socio-emotional and cognitive capacities. Key social and affective interactions, such as communication, cooperative play and the establishment of specific attachments propel the development of the parent–infant relationship. We summarise our current knowledge of the developing infant brain in terms of structure and function, and how these relate to the emergent abilities necessary for the formation of a secure and cooperative relationship with parents or other caregivers. Important roles have been found for brain regions including the orbitofrontal, cingulate, and insular cortices in parent–infant interactions, but it has become clear that much more information is needed about the developmental time course and connectivity of these regions.

India’s disappearing common lands: fuzzy boundaries, encroachment, and evolving property rights

Opportunistic land encroachment occurs in many low-income countries, gradually yet pervasively, until discrete areas of common land disappear. This paper, motivated by field observations in Karnataka, India, demonstrates that such an evolution of property rights from common to private may be efficient when the boundaries between common and private land are poorly defined, or ‘‘fuzzy.’’ Using a multi-period optimization model, and introducing the concept of stock and flow enforcement, I show how effectiveness of enforcement effort, whether encroachment is reversible, and punitive fines, influence whether an area of common land is fully defined and protected or gradually or rapidly encroached.

Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.

TRCM: a methodology for temporal analysis of evolving concepts in Twitter

The Twitter network has been labelled the most commonly used microblogging application around today. With about 500 million estimated registered users as of June, 2012, Twitter has become a credible medium of sentiment/opinion expression. It is also a notable medium for information dissemination; including breaking news on diverse issues since it was launched in 2007. Many organisations, individuals and even government bodies follow activities on the network in order to obtain knowledge on how their audience reacts to tweets that affect them. We can use postings on Twitter (known as tweets) to analyse patterns associated with events by detecting the dynamics of the tweets. A common way of labelling a tweet is by including a number of hashtags that describe its contents. Association Rule Mining can find the likelihood of co-occurrence of hashtags. In this paper, we propose the use of temporal Association Rule Mining to detect rule dynamics, and consequently dynamics of tweets. We coined our methodology Transaction-based Rule Change Mining (TRCM). A number of patterns are identifiable in these rule dynamics including, new rules, emerging rules, unexpected rules and ?dead' rules. Also the linkage between the different types of rule dynamics is investigated experimentally in this paper.

Tropical Atlantic variability modes (1979–2002). Part I: Time-evolving SST modes related to West African rainfall

This work presents a description of the 1979–2002 tropical Atlantic (TA) SST variability modes coupled to the anomalous West African (WA) rainfall during the monsoon season. The time-evolving SST patterns, with an impact on WA rainfall variability, are analyzed using a new methodology based on maximum covariance analysis. The enhanced Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) dataset, which includes measures over the ocean, gives a complete picture of the interannual WA rainfall patterns for the Sahel dry period. The leading TA SST pattern, related to the Atlantic El Niño, is coupled to anomalous precipitation over the coast of the Gulf of Guinea, which corresponds to the second WA rainfall principal component. The thermodynamics and dynamics involved in the generation, development, and damping of this mode are studied and compared with previous works. The SST mode starts at the Angola/Benguela region and is caused by alongshore wind anomalies. It then propagates westward via Rossby waves and damps because of latent heat flux anomalies and Kelvin wave eastward propagation from an off-equatorial forcing. The second SST mode includes the Mediterranean and the Atlantic Ocean, showing how the Mediterranean SST anomalies are those that are directly associated with the Sahelian rainfall. The global signature of the TA SST patterns is analyzed, adding new insights about the Pacific– Atlantic link in relation to WA rainfall during this period. Also, this global picture suggests that the Mediterranean SST anomalies are a fingerprint of large-scale forcing. This work updates the results given by other authors, whose studies are based on different datasets dating back to the 1950s, including both the wet and the dry Sahel periods.

Primary evolving networks and the comparative analysis of robust and fragile structures

In this paper we consider the structure of dynamically evolving networks modelling information and activity moving across a large set of vertices. We adopt the communicability concept that generalizes that of centrality which is defined for static networks. We define the primary network structure within the whole as comprising of the most influential vertices (both as senders and receivers of dynamically sequenced activity). We present a methodology based on successive vertex knockouts, up to a very small fraction of the whole primary network,that can characterize the nature of the primary network as being either relatively robust and lattice-like (with redundancies built in) or relatively fragile and tree-like (with sensitivities and few redundancies). We apply these ideas to the analysis of evolving networks derived from fMRI scans of resting human brains. We show that the estimation of performance parameters via the structure tests of the corresponding primary networks is subject to less variability than that observed across a very large population of such scans. Hence the differences within the population are significant.