Bio-inspired paradigms are proving to be useful in analysing propagation and dissemination of information in networks. In this paper we explore the use of multi-type branching processes to analyse viral properties of content in a social network, with and without competition from other sources. We derive and compute various virality measures, e.g., probability of virality, expected number of shares, or the rate of growth of expected number of shares etc. They allow one to predict the emergence of global macro properties (e.g., viral spread of a post in the entire network) from the laws and parameters that determine local interactions. The local interactions, greatly depend upon the structure of the timelines holding the content and the number of friends (i.e., connections) of users of the network. We then formulate a non-cooperative game problem and study the Nash equilibria as a function of the parameters. The branching processes modelling the social network under competition turn out to be decomposable, multi-type and continuous time variants. For such processes types belonging to different sub-classes evolve at different rates and have different probabilities of extinction etc. We compute content provider wise extinction probability, rate of growth etc. We also conjecture the content-provider wise growth rate of expected shares.

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In this research, the failure mechanism and anomalous behavior of intact and jointed rock block having a circular tunnel under compression are studied. This was done by monitoring the progressive failure of a rock tunnel subjected to uniaxial loading. The tests were conducted in sandstone blocks and “Acoustic Emission” (AE) technique was used to identify the crack damage and other failure attributes. Three cases have been considered in the research, i.e. tunnel in the intact rock, with horizontal joints, and with vertical joint sets. Images of progressive failure, acoustic signals, and applied loads were simultaneously recorded during the test. The intact block demonstrates continuous crack generation while the block with horizontal joint set shows a stepwise cracking pattern. In the third case where the vertical joints were employed, the deformation was largely roof failure and joint perpendicular extension was dominant. The AE events show that a sudden drop and then a quiet period of seismic “Ib value” could be considered as the precursors to forecast the rockburst hazard. The paper also compares the results of the physical model test with a 2D finite element model. The compared results show good agreement between the physical and numerical models.

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