In this paper, we propose DyPerm, the first dynamic community detection method which optimizes a novel community scoring metric, called permanence. DyPerm incrementally modifies the community structure by updating those communities where the editing of nodes and edges has been performed, keeping the rest of the network unchanged. We present strong theoretical guarantees to show how/why mere updates on the existing community structure leads to permanence maximization in dynamic networks, which in turn decreases the computational complexity drastically. Experiments on both synthetic and six real-world networks with given ground-truth community structure show that DyPerm achieves (on average) 35% gain in accuracy (based on NMI) compared to the best method among four baseline methods. DyPerm also turns out to be 15 times faster than its static counterpart. 1 final communities [16,23]. In this paper, we propose DyPerm, the first dynamic community detection method that adopts an effective community goodness metric, called "permanence" [12,13,9] and optimizes it to incrementally detect the community structure. The benefits of adopting permanence as an optimization function are two-fold: (i) Permanence, being a local vertex-centric metric (as opposed to the global network-centric metrics such as modularity, conductance), allows us to reassign communities to only those nodes whose associated topological structure has changed, and guarantees that the remaining nodes do not affect the optimization. This leads to very low computing complexity in updating the community structure when the network changes dynamically. (ii) Incremental changes in the local portion of the community structure guarantee that the resultant communities are highly correlated with that in the previous time-stamp. We present theoretical justifications why/how mere changes in the community structure lead to maximize permanence.We experiment with both synthetic and six real-world dynamic networks with known ground-truth community structure. A thorough comparative evaluation with four state-of-the-art baseline methods shows that DyPerm significantly outperforms all the baselines across different networks -DyPerm achieves up to 35% improvement in terms of Normalized Mutual Information (NMI) w.r.t. the best baseline method. Moreover, DyPerm tunrs out to be extremely fast, achieving up to 15 times speedup w.r.t. its static counterpart. In short, DyPerm is a fast and accurate dynamic community detection method.

When sound waves of high amplitude propagate, several non-linear effects occur. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter of four binary liquid mixtures using Tong and Dong equation at high pressures and Ì ¿¼¿ ½ K. Thermodynamic method has also been used to calculate the non-linearity parameter after making certain approximations.

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